Algebra Examples

$f (x) = \frac{4}{5} x - 3$ , $g (x) = \frac{5 x + 15}{4}$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (\frac{4}{5} x - 3)$ by substituting in the value of $f$ into $g$ .

$g (\frac{4}{5} x - 3) = \frac{5 (\frac{4}{5} x - 3) + 15}{4}$

Step 3

Simplify the numerator.

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Step 3.1

Factor $5$ out of $5 (\frac{4}{5} x - 3) + 15$ .

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Step 3.1.1

Factor $5$ out of $15$ .

$g (\frac{4}{5} x - 3) = \frac{5 (\frac{4}{5} x - 3) + 5 \cdot 3}{4}$

Step 3.1.2

Factor $5$ out of $5 (\frac{4}{5} x - 3) + 5 \cdot 3$ .

$g (\frac{4}{5} x - 3) = \frac{5 (\frac{4}{5} x - 3 + 3)}{4}$

Step 3.2

Combine $\frac{4}{5}$ and $x$ .

$g (\frac{4}{5} x - 3) = \frac{5 (\frac{4 x}{5} - 3 + 3)}{4}$

Step 3.3

Add $- 3$ and $3$ .

$g (\frac{4}{5} x - 3) = \frac{5 (\frac{4 x}{5} + 0)}{4}$

Step 3.4

Add $\frac{4 x}{5}$ and $0$ .

$g (\frac{4}{5} x - 3) = \frac{5 (\frac{4 x}{5})}{4}$

Step 4

Combine $5$ and $\frac{4 x}{5}$ .

$g (\frac{4}{5} x - 3) = \frac{\frac{5 (4 x)}{5}}{4}$

Step 5

Multiply $5$ by $4$ .

$g (\frac{4}{5} x - 3) = \frac{\frac{20 x}{5}}{4}$

Step 6

Reduce the expression by cancelling the common factors.

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Step 6.1

Reduce the expression $\frac{20 x}{5}$ by cancelling the common factors.

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Step 6.1.1

Factor $5$ out of $20 x$ .

$g (\frac{4}{5} x - 3) = \frac{\frac{5 (4 x)}{5}}{4}$

Step 6.1.2

Factor $5$ out of $5$ .

$g (\frac{4}{5} x - 3) = \frac{\frac{5 (4 x)}{5 (1)}}{4}$

Step 6.1.3

Cancel the common factor.

$g (\frac{4}{5} x - 3) = \frac{\frac{5 (4 x)}{5 \cdot 1}}{4}$

Step 6.1.4

Rewrite the expression.

$g (\frac{4}{5} x - 3) = \frac{\frac{4 x}{1}}{4}$

Step 6.2

Divide $4 x$ by $1$ .

$g (\frac{4}{5} x - 3) = \frac{4 x}{4}$

Step 7

Cancel the common factor of $4$ .

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Step 7.1

Cancel the common factor.

$g (\frac{4}{5} x - 3) = \frac{4 x}{4}$

Step 7.2

Divide $x$ by $1$ .

$g (\frac{4}{5} x - 3) = x$