Which two functions are inverses of each other? f(x)= x, g(x) = -x f(x)= 2x, g(x) = - 1/2x f(x) = 4x, g(x) = 1/4x f(x) = -8x, g(x) = 8x

Question

asked Oct 11, 2020 214k views

2 Answers

Jmesnil · Answer 1 · 2020-10-16T04:26:13+0000

Answer:

Option 3 - f(x)= 4x,
g(x) = (1)/(4)x

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

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

Not true.

2) f(x)= 2x,
g(x) = -(1)/(2)x

$f(g(x))=f(-(1)/(2)x)=2*(-(1)/(2)x)=-x\\eq x$

Not true.

3) f(x)= 4x,
g(x) = (1)/(4)x

f(g(x))=f((1)/(4)x)=4*((1)/(4)x)=x

g(f(x))=f(4x)=(1)/(4)* 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

$f(g(x))=f(8x)=8*(-8x)=-64x\\eq x$

Not true.

Therefore, Option 3 is correct.