Please help with this question on functions?

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Please help with this question on functions?

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Answer 1 · 2018-04-30T16:33:29

See below

Explanation:

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

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

The question really states, when translated into words that:

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

Thus;

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

Hence in 1.:

$f (7) = 3 (7) - 5 = 21 - 5 = 16$ $f(7)=3(7)-5=21-5=16$

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

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

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

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

Answer 2 · 2018-04-30T16:38:13

16
16
9

Explanation:

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

$f (4) \Rightarrow$ $f(4) =>$ substitute $x = 4$ $x=4$ into $x^{2} = 4^{2} = 16$ $x^2=4^2=16$
because $x = 4$ $x=4$

$f (- 3) \Rightarrow$ $f(-3) =>$ substitute $x = - 3$ $x=-3$ into $x^{2} = {(- 3)}^{2} = 9$ $x^2=(-3)^2=9$
because $x < 4$ $x<4$

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Please help with this question on functions?

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