Apr 30, 2018

See below

#### Explanation:

The way I interpret the question is that you have the function
$f \left(x\right)$, each with its own restricted domain.

Domain= the values $x$ is allowed to take in the function.

The question really states, when translated into words that:

Given the function $f \left(x\right) ,$ where if $x$ is greater than 4, the function of $f$ is equal to 3x-5. If instead $x$ is less than or equal to 4 then a function of $x$ is equal to ${x}^{2}$.

Thus;

1. If $x$ is greater than 4, apply $f \left(x\right) = 3 x - 5$
2.If $x$ is less than or equal to 4, apply $f \left(x\right) = {x}^{2}$

Hence in 1.:

$f \left(7\right) = 3 \left(7\right) - 5 = 21 - 5 = 16$

For 2.:
$f \left(4\right) = {4}^{2} = 16$

As the equation states that $f \left(x\right) = {x}^{2}$ applies if $x$ is less than OR equal to $4$.

For 3.: $4 > x$ as $x = - 3$ so we must apply the first function.

$f \left(- 3\right) = {\left(- 3\right)}^{2} = 9$

Apr 30, 2018
1. 16
2. 16
3. 9

#### Explanation:

$f \left(7\right) \implies$ substitute $x = 7$ into $3 x - 5 = 21 - 5 = 16$
because $x > 4$

$f \left(4\right) \implies$ substitute $x = 4$ into ${x}^{2} = {4}^{2} = 16$
because $x = 4$

$f \left(- 3\right) \implies$ substitute $x = - 3$ into ${x}^{2} = {\left(- 3\right)}^{2} = 9$
because $x < 4$