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swat32
3 years ago
7

What is the inverse of the function f(x)=1/9x+2

Mathematics
2 answers:
Anna35 [415]3 years ago
7 0

Answer:

f^{-1}(x)=9x-18

Step-by-step explanation:

we have

f(x)=\frac{1}{9}x+2

Let

y=f(x)

y=\frac{1}{9}x+2

Exchange variables x for y and y for x

x=\frac{1}{9}y+2

Isolate the variable y

x-2=\frac{1}{9}y

y=9(x-2)

y=9x-18

Let

f^{-1}(x)=y

f^{-1}(x)=9x-18 -------> inverse function

MrRissso [65]3 years ago
6 0
F(x) = 1/9x+2

-2 from both sides

f(x)-2 = 1/9x

*2 to both sides

9(f(x)-2) = x

replace 'f(x)' with 'x'

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

simplify and reverse sides

f(x)^-1 = 9x-18
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