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The functions [tex]\( f \)[/tex] and [tex]\( g \)[/tex] are defined as follows:

[tex]\[ f(x) = 5x + 4 \][/tex]
[tex]\[ g(x) = 3x^3 + 5 \][/tex]

Find [tex]\( f(-3) \)[/tex] and [tex]\( g(-2) \)[/tex]. Simplify your answers as much as possible.

[tex]\[ f(-3) = \ \square \][/tex]
[tex]\[ g(-2) = \ \square \][/tex]

Sagot :

GinnyAnswer
Sure, let's solve for [tex]\( f(-3) \)[/tex] and [tex]\( g(-2) \)[/tex] using the given functions step-by-step.

Starting with [tex]\( f(x) = 5x + 4 \)[/tex]:

1. To find [tex]\( f(-3) \)[/tex], substitute [tex]\( x = -3 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[ f(-3) = 5(-3) + 4 \][/tex]
2. Now, calculate the value:
[tex]\[ f(-3) = -15 + 4 \][/tex]
3. Simplify the expression:
[tex]\[ f(-3) = -11 \][/tex]

Next, for [tex]\( g(x) = 3x^3 + 5 \)[/tex]:

1. To find [tex]\( g(-2) \)[/tex], substitute [tex]\( x = -2 \)[/tex] into the function [tex]\( g(x) \)[/tex]:
[tex]\[ g(-2) = 3(-2)^3 + 5 \][/tex]
2. Now, calculate the value of [tex]\((-2)^3\)[/tex]:
[tex]\[ (-2)^3 = -8 \][/tex]
3. Substitute back into the function:
[tex]\[ g(-2) = 3(-8) + 5 \][/tex]
4. Calculate the resulting value:
[tex]\[ g(-2) = -24 + 5 \][/tex]
5. Simplify the expression:
[tex]\[ g(-2) = -19 \][/tex]

So, the solutions are:
[tex]\[ f(-3) = -11 \][/tex]
[tex]\[ g(-2) = -19 \][/tex]
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