# Graphs - Inverse Functions

a - answer    s - solution    v - video    d - discussion

## Question 1

Find $f(x)$

a) $f(x)=2x$ when $x=3$a s v d
b) $f(x)=\frac x5$ when $x=20$a s v d
c) $f(x)=x+16$ when $x=12$a s v d
d) $f(x)=x-3$ when $x=10$a s v d
e) $f(x)=3x+11$ when $x=4$a s v d
f) $f(x)=\frac x6-2$ when $x=18$a s v d
g) $f(x)=x^2+5$ when $x=2$a s v d
h) $f(x)=3-\sqrt x$ when $x=36$a s v d

## Question 2

Find the inverse function for the following functions

a) $f(x)=x+2$a s v d
b) $g(x)=x-5$a s v d
c) $h(x)=3x$a s v d
d) $p(x)=x\div6$a s v d
e) $q(x)=\frac x9$a s v d
f) $f(y)=y+t$a s v d
g) $g(a)=\frac ab$a s v d
h) $h(z)=\sqrt z$a s v d
i) $p(x)=x^5$a s v d
j) $m(r)=-r$a s v d
k) $f(x)=\frac1x$a s v d

## Question 3

Show that the following are the inverse when $x=4$

a) $f(x)=x^3$ and $f^{-1}(x)=\sqrt[3] x$a s v d
b) $f(x)=2+3x$ and $f^{-1}(x)=\frac{x-2}{3}$a s v d
c) $f(x)=\frac{2+x}{4}$ and $f^{-1}(x)=4x-2$a s v d
d) $g(x)=\sqrt{x+12}-3$ and $g^{-1}(x)={(x+3)}^2-12$a s v d
e) $h(x)=\sqrt{x+12}-3$ and $h^{-1}(x)={(x+3)}^2-12$a s v d
f) $q(x)=\frac1x$ and $q^{-1}(x)=\frac1x$a s v d
g) $p(x)=\frac14x-7$ and $p^{-1}(x)=4(x+7)$a s v d
h) $f(x)=\frac{(2x+3)^2}{11}$ and $f^{-1}(x)=\frac{\sqrt{11x}-3}{2}$a s v d

## Question 4

Find the inverse function for the following functions

a) $f(x)=2x+3$a s v d
b) $f(x)=-5x+6$a s v d
c) $f(x)=\frac12x-3$a s v d
d) $g(x)=\frac15x+\frac23$a s v d
e) $f(x)=\frac{x+1}{4}$a s v d
f) $n(x)=\frac{x-2}{-5}$a s v d
g) $f(a)=\sqrt a+15$a s v d
h) $g(y)={(y+3)}^3$a s v d

## Question 5

By showing that $f(f^{-1}(x))=x$ prove that the following inverse functions are given:

a) $f(x)=2x$ and $f^{-1}(x)=\frac x2$a s v d
b) $f(x)=\frac14x$ and $f^{-1}(x)=4x$a s v d
c) $f(x)=4x-1$ and $f^{-1}(x)=\frac{x+1}{4}$a s v d
d) $f(x)=\sqrt{5x}+4$ and $f^{-1}(x)=\frac{{(x-4)}^2}{5}$a s v d
e) $f(x)=\frac{x+4}{2x-5}$ and $f^{-1}(x)=\frac{5x+4}{2x-1}$a s v d