Question

Which two functions are inverses of each other?

Answer 1

Answer:

Option 3 - f(x)= 4x, $g(x) = \frac{1}{4}x$

Step-by-step explanation:

To find : Which two functions are inverses of each other?

Solution :

Two functions are inverse if $f(g(x))=x=g(f(x))$

Now, we find one by one

1) f(x)= x, g(x) = -x

$f(g(x))=f(-x)=-x\neq x$

Not true.

2) f(x)= 2x, $g(x) = -\frac{1}{2}x$

$f(g(x))=f(-\frac{1}{2}x)=2\times(-\frac{1}{2}x)=-x\neq x$

Not true.

3) f(x)= 4x, $g(x) = \frac{1}{4}x$

$f(g(x))=f(\frac{1}{4}x)=4\times(\frac{1}{4}x)=x$

$g(f(x))=f(4x)=\frac{1}{4}\times 4x=x$

i.e. $f(g(x))=x=g(f(x))$ is true.

So, These two functions are inverse of each other.

4) f(x)= -8x, $g(x) =8x$

$f(g(x))=f(8x)=8\times(-8x)=-64x\neq x$

Not true.

Therefore, Option 3 is correct.