Question

Easy - Math - INVERSES - NEED ASAP PLEASE AND THANK YOU VERY MUCH!

Answer 1

Answer:

Part 1) No

Part 2) Option 4. $f^{-1}(x)=-\frac{1}{3}x+3$

part 3) $f^{-1}(9)=4$

Step-by-step explanation:

Part 1) we have

$f(x)=8x-3$

$g(x)=(x+8)/3$  

Find the inverse of f(x) and then compare with g(x)

Let

y=f(x)

$y=8x-3$

Exchange the variables x for y and y for x

$x=8y-3$

Isolate the variable y

$8y=(x+3)$

$y=(x+3)/8$

Let

$f^{-1}(x)=y$

$f^{-1}(x)=(x+3)/8$

therefore

the functions f(x) and g(x) are not inverses of each other

Part 2) we have

$f(x)=-3x+9$

Let

y=f(x)

$y=-3x+9$

Exchange the variables x for y and y for x

$x=-3y+9$

Isolate the variable y

$3y=-x+9$

$y=(-x+9)/3$

Let

$f^{-1}(x)=y$

$f^{-1}(x)=(-x+9)/3$

$f^{-1}(x)=-\frac{1}{3}x+3$

Part 3) we know that

For $x=4$, $f(x)=9$

so

For $x=9$, $f^{-1}(9)=4$