Given f(x)=6x^4, find f^-1(x). Then state whether f^-1(x) is a function.

Question

asked Jun 21, 2018 207k views

2 Answers

David Lilljegren · Answer 1 · 2018-06-26T01:58:34+0000

Answer:

$f^(-1)(x)=((x)/(6))^{(1)/(4)}$

This is a function for [0,∞).

Explanation:

The given function is

f(x)=6x^4

We need to find the
f^(-1)(x) .

Step 1: Replace f(x) be y.

y=6x^4

Step 2: Interchange x and y.

x=6y^4

Step 3: Isolate variable y.

(x)/(6)=y^4

$((x)/(6))^{(1)/(4)}=y$

Step 4: Interchange the sides.

$y=((x)/(6))^{(1)/(4)}$

Step 5: Replace y by
f^(-1)(x) .

$f^(-1)(x)=((x)/(6))^{(1)/(4)}$

Therefore,
$f^(-1)(x)=((x)/(6))^{(1)/(4)}$ .

This function is is defined for all positive values of x.

The inverse of function
f(x)=6x^4 is a function for [0,∞).