Answer:
f( -2) = 11
g(5) = - 18
Step-by-step explanation:
#1. Solving for f(-2)
We're given a function "f" such that when it accepts a variable x, it's output, f(x), is:
[tex] \boxed{ \mathsf{f(x) = - 2 {x}^{3} - 5}}[/tex]
The value of f(x) depends upon what value of x is being inserted.
If x = -2
All the places taken by x will be given to -2
[tex] \implies \mathsf{f( - 2) = - 2( { - 2}^{3} )- 5 }[/tex]
(-2)³ is the cube of (-2) with -8 as it's result
[tex] \implies \mathsf{f( - 2) = - 2( { - 8}^{} )- 5 }[/tex]
when there's no operating sign between two numbers from different origin, they're multiplied
[tex] \implies \mathsf{f( - 2) = 16 - 5 }[/tex]
[tex] \implies \mathsf{f( - 2) = 11 }[/tex]
That gives us the value of f(-2) :
11
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#2. Solving for g(5):
Here's another function, "g", taking x as input and giving us an output g(x), such that:
[tex] \boxed{ \mathsf{g(x) = - 4x + 2}}[/tex]
If x = 5
All the positions taken by x will be given to 5:
[tex] \implies \mathsf{g(5) = - 4(5) + 2}[/tex]
no sign between two numbers from different origin results in their product.
[tex] \implies \mathsf{g(5) = - 20+ 2}[/tex]
[tex] \implies \mathsf{g(5) = - 18}[/tex]
Thus, the value of g(5) is:
-18
