Evaluating and Interpreting Function Notation

a

Using the function $f (x),$ we want to evaluate for the given value, $5 (f (n)) .$ There are two steps involved in this evaluation.

Let's first take care of the substitution. To do this, we need to substitute

n

for

x

in each instance of the

x

-variable.

f (x) = - 5 x + 2 \Rightarrow f (n) = - 5 n + 2

Now we can multiply the function by

5 .

f (n) = - 5 n + 2

LHS \cdot 5 = RHS \cdot 5

5 (f (n)) = 5 (- 5 n + 2)

DistrDistribute

5

5 (f (n)) = - 25 n + 10

We are finished and have found that

5 (f (n)) = - 25 n + 10 .

b

We have the function

g (x) = 3 x^{2}

and want to find

- 2 (g (p)) .

We will do it in two steps. In the first step

g (x)

is evaluated for

p .

We will do that by substituting

p

for

x

in the function rule.

g (x) = 3 x^{2} \Rightarrow g (p) = 3 p^{2}

Next step is to multiply the function by

- 2 .

g (p) = 3 p^{2}

LHS \cdot (- 2) = RHS \cdot (- 2)

- 2 (g (p)) = - 2 (3 p^{2})

- 2 (g (p)) = - 6 x^{2}

Above we have shown that

- 2 (g (p)) = - 6 x^{2} .

Evaluating and Interpreting Function Notation 1.14 - Solution