Algebra Examples

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

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (\frac{1}{4} x + \frac{1}{4})$ by substituting in the value of $g$ into $f$ .

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

Step 3

Simplify each term.

Tap for more steps...

Step 3.1

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

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

Step 3.2

Apply the distributive property.

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

Step 3.3

Cancel the common factor of $4$ .

Tap for more steps...

Step 3.3.1

Cancel the common factor.

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

Step 3.3.2

Rewrite the expression.

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

Step 3.4

Cancel the common factor of $4$ .

Tap for more steps...

Step 3.4.1

Cancel the common factor.

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

Step 3.4.2

Rewrite the expression.

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

Step 4

Combine the opposite terms in $x + 1 - 1$ .

Tap for more steps...

Step 4.1

Subtract $1$ from $1$ .

$f (\frac{1}{4} x + \frac{1}{4}) = x + 0$

Step 4.2

Add $x$ and $0$ .

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