Answered

The functions [tex]f, g[/tex], and [tex]h[/tex] are defined as follows:
[tex]\[ f(x) = -4 + \sqrt{-2 + x} \][/tex]
[tex]\[ g(x) = 2|-4 + x| \][/tex]
[tex]\[ h(x) = \frac{-4x^2 + 6}{x^2} \][/tex]

Find [tex]f(7), g(-3)[/tex], and [tex]h(-2)[/tex].

Simplify your answers as much as possible.

[tex]\[ \begin{array}{c}
f(7) = \\
g(-3) = \\
h(-2) =
\end{array} \][/tex]

[tex]\square[/tex]
[tex]\square[/tex]
[tex]\square[/tex]



Answer :

GinnyAnswer
Let's find each of the values step-by-step.

### Finding [tex]\( f(7) \)[/tex]:
Given the function:
[tex]\[ f(x) = -4 + \sqrt{-2 + x} \][/tex]

Substitute [tex]\( x = 7 \)[/tex]:
[tex]\[ f(7) = -4 + \sqrt{-2 + 7} \][/tex]
[tex]\[ f(7) = -4 + \sqrt{5} \][/tex]

So,
[tex]\[ f(7) \approx -1.7639320225002102 \][/tex]

### Finding [tex]\( g(-3) \)[/tex]:
Given the function:
[tex]\[ g(x) = 2 \left| -4 + x \right| \][/tex]

Substitute [tex]\( x = -3 \)[/tex]:
[tex]\[ g(-3) = 2 \left| -4 + (-3) \right| \][/tex]
[tex]\[ g(-3) = 2 \left| -7 \right| \][/tex]
[tex]\[ g(-3) = 2 \cdot 7 \][/tex]
[tex]\[ g(-3) = 14 \][/tex]

So,
[tex]\[ g(-3) = 14 \][/tex]

### Finding [tex]\( h(-2) \)[/tex]:
Given the function:
[tex]\[ h(x) = \frac{-4 x^2 + 6}{x^2} \][/tex]

Substitute [tex]\( x = -2 \)[/tex]:
[tex]\[ h(-2) = \frac{-4 (-2)^2 + 6}{(-2)^2} \][/tex]
[tex]\[ h(-2) = \frac{-4 \cdot 4 + 6}{4} \][/tex]
[tex]\[ h(-2) = \frac{-16 + 6}{4} \][/tex]
[tex]\[ h(-2) = \frac{-10}{4} \][/tex]
[tex]\[ h(-2) = -2.5 \][/tex]

So,
[tex]\[ h(-2) = -2.5 \][/tex]

Combining all the results:
[tex]\[ \begin{array}{c} f(7) \approx -1.7639320225002102 \\ g(-3) = 14 \\ h(-2) = -2.5 \\ \end{array} \][/tex]