If f: A ⟶ B and g: B ⟶ C are functions . If g is...

Question

Question

If f: A ⟶ B and g: B ⟶ C are functions . If g is onto, then g ∘ f : A ⟶ C is onto

Group of answer choices

True

False

math Statistics-And-Probability

Answer 1

Answer #1

Here g: B ⟶ C is onto i.e, every element in set C has at least one element as an image in set B

But this does not assure that every element in the set B will have at least one element as an image in the set A

And because of this, it is not sure that every element in the set C will have at least one element as an image in the set A

Therefore

If g is onto, then g ∘ f : A ⟶ C is not necessarily onto

Answer: False.

Please give thumbs up if you like the answer.

Answer 2

Similar Homework Help Questions

Let f : A rightarrow D and g : B rightarrow C be functions. For each...

Let f : A rightarrow D and g : B rightarrow C be functions. For each part, if the answer is yes, then prove it, otherwise give a counterexample. Suppose f is one-to-one (injective) and g is onto (surjective). Is go f one-to-one (injective)? Suppose f is one-to-one (injective) and g is onto (surjective). Is g f onto (surjective)? Suppose g is one-to one. Is g one-to-one? Suppose g f onto. Is g onto?
True or False: If f(x) and g(x) are two differentiable functions on an interval (a,b), and...

True or False: If f(x) and g(x) are two differentiable functions on an interval (a,b), and f(x)>g(x) on (a,b), then f'(x)>g'(x).
Answer Choices: A) A, B B) F, G C) C, D, F, G D) F Required...

Answer Choices: A) A, B B) F, G C) C, D, F, G D) F Required information Fruit flies normally have red eyes. Seven different true-breeding strains of fly with white eyes have been identified (A-G). In each strain, the white eye trait is due to an autosomal recessive allele. It is possible all seven strains have mutations in the same gene. Alternatively, they may have mutations in different genes. To determine how many genes are involved in eye color...

11. Circle true or false. No justification is needed. (14 points) (a) If f(x) - o(g(x), and both functions are continuous and positive, then fix dz converges. TRUE FALSE (b) If f(x)- o(g(x)), the...

11. Circle true or false. No justification is needed. (14 points) (a) If f(x) - o(g(x), and both functions are continuous and positive, then fix dz converges. TRUE FALSE (b) If f(x)- o(g(x)), then f(x)gx)~g(x). TRUE FALSE (c) If the power series Σ an(x + 2)" converges atェ= 5, then it must km0 converge at =-6. TRUE FALSE (d) There exists a power series Σ akz" which converges to f(z)-I on some interval of positive length around FALSE TRUE (e)...
Let f: A ⟶ B be a function. If f is bijection then f − 1 is a bijective...

Let f: A ⟶ B be a function. If f is bijection then f − 1 is a bijective function from B to A. Group of answer choices True False
Suppose f, g are two functions mapping positive real numbers to positive real numbers and f...

Suppose f, g are two functions mapping positive real numbers to positive real numbers and f = O(g). Prove why each statement is true or false. (a) log2 f = O(log2 g) (b) √f = O(f) (c) fk + 100fk−1 = O(gk), for k ≥ 1

1. (a) (6 points) Let f : A + B and g:B + C be two...

1. (a) (6 points) Let f : A + B and g:B + C be two functions. Suppose that the composition of functions go f is a bijection. Prove that the function f : A + B must be one-to-one and that the function g:B + C must be onto. (b) (4 points) Give an example of a pair of functions, f and g, such that the composition gof is a bijection, but f is not onto and g is...
5. (a) Show that if the functions f and g are log-convex, f+g is also log-convex....

5. (a) Show that if the functions f and g are log-convex, f+g is also log-convex. Give a counter example to show that this is not true for log-concave functions (Hint: log(f +g)log(elogf +elogs). Show that this is convex by the second-order test for convexity.) (Hint: Use the definition of log-convex functions.) (Note: Harmonic mean of a,b is defined as T^T.) b) Suppose f is convex, g is non-decreasing and log-convex. Show that h(x) g(f(x)) is log-convex. (c) Show that...
Use the functions f and g in C[-1, 1] to find (f, g), ||f||| ||9||, and...

Use the functions f and g in C[-1, 1] to find (f, g), ||f||| ||9||, and d(f, g) for the inner product (5, 8) - [F f(x)g(x)dx. f(x) = 1, g(x) = 7x2 - 1 (a) (f. 9) (b) ||fl| (c) |19|| (d) df, g)

1. Let f and g be functions with the same domain and codomain (let A be...

1. Let f and g be functions with the same domain and codomain (let A be the domain and B be the codomain). Consider the following ordered triple h = (A, B, f LaTeX: \cap ∩ g) (Note: The f and g in the triple refer to the "rules" associated with the functions f and g). Prove that h is a function. Would the same thing be true if, instead of intersection, we had a union? If your answer is...