Find g(f(x)) f(x)=4x-1 ; g(x)=1/4x+1/4

$f (x) = 4 x - 1$ ; $g (x) = \frac{1}{4} x + \frac{1}{4}$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (4 x - 1)$ by substituting in the value of $f$ into $g$ .

$g (4 x - 1) = \frac{1}{4} \cdot (4 x - 1) + \frac{1}{4}$

Step 3

Simplify each term.

Apply the distributive property.

$g (4 x - 1) = \frac{1}{4} \cdot (4 x) + \frac{1}{4} \cdot - 1 + \frac{1}{4}$

Cancel the common factor of $4$ .

Factor $4$ out of $4 x$ .

$g (4 x - 1) = \frac{1}{4} \cdot (4 (x)) + \frac{1}{4} \cdot - 1 + \frac{1}{4}$

Cancel the common factor.

$g (4 x - 1) = \frac{1}{4} \cdot (4 x) + \frac{1}{4} \cdot - 1 + \frac{1}{4}$

Rewrite the expression.

$g (4 x - 1) = x + \frac{1}{4} \cdot - 1 + \frac{1}{4}$

Combine $\frac{1}{4}$ and $- 1$ .

$g (4 x - 1) = x + \frac{- 1}{4} + \frac{1}{4}$

Move the negative in front of the fraction.

$g (4 x - 1) = x - \frac{1}{4} + \frac{1}{4}$

Step 4

Combine the opposite terms in $x - \frac{1}{4} + \frac{1}{4}$ .

Add $- \frac{1}{4}$ and $\frac{1}{4}$ .

$g (4 x - 1) = x + 0$

Add $x$ and $0$ .

$g (4 x - 1) = x$