If $f ( x ) = \sqrt { x }$ and $g ( x ) =$ __________, then $( g \circ f ) ( x ) = 3 x - 1$

Question

Quizplus · Accepted Answer

The Answer is To find the function

g(x)

such that

(g \circ f)(x) = 3x - 1

, we need to understand that the composition of functions

(g \circ f)(x)

means applying the function

f

to

x

first, and then applying the function

g

to the result of

f(x)

.

Given

f(x) = \sqrt{x}

, we want to find

g(x)

such that when we apply

g

to

f(x)

, we get

3x - 1

.

Let's denote

y = f(x) = \sqrt{x}

. Then, we want to find

g(y)

such that

g(y) = 3x - 1

.

Since

y = \sqrt{x}

, we can square both sides to find

x

:

y^2 = (\sqrt{x})^2

y^2 = x

Now, we substitute

y^2

for

x

in the equation

g(y) = 3x - 1

:

g(y) = 3y^2 - 1

Therefore, the function

g(x)

that satisfies the condition

(g \circ f)(x) = 3x - 1

is:

g(x) = 3x^2 - 1

If f(x)=xf ( x ) = \sqrt { x }f(x)=x​ And g(x)=g ( x ) =g(x)=