Question

4) Let f(x) = 2*-2 + 1 a) Graph f(x). Describe the transformations that you make to 24 to obtain the graph of f(x) b) f(x) has an inverse, f'(x). Find f-'(x) c) Graph f-'(x).

Answer 1

4)

f(x)=2^x-2+1

a)

x	0	1	2	3	4
f(x)	1.25	1.5	2	3	5

f(x) = 27-2+1 y-axis -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 x-axis 4 5 6 7

shift the graph of y=2^x horizontally 2 units to the right and vertically upwards by 1 unit to get graph of
f(x)=2^x-2+1

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b)

let f(x)=y
=>x=f^-1(y)

2^x-2+1=y
=>2^x-2=y-1
=>x-2=log₂(y-1)
=>x=2+log₂(y-1)
=>f^-1(y)=2+log₂(y-1)
=>f^-1(x)=2+log₂(x-1)

c)

x	1.25	2	3	5
f-1(x)	0	2	3	4

> y= 2 + log, (x - 1) y-axis 6 -5 -4 -3 -2 -1 1 2 3 4 5 x-axis 6 7 8 9 10 1

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