Answer :
[tex]\(f(g(-3))\)[/tex] is equal to c. [tex]\(23\)[/tex]. [tex]\( f(h(7)) \)[/tex] is equal to d. [tex]\( 442 \)[/tex].
To evaluate the expression [tex]\(f(g(-3))\)[/tex], you first need to find the value of [tex]\(g(-3)\)[/tex] and then substitute that value into the function [tex]\(f(x)\)[/tex].
Given that [tex]\(g(x) = x^2 + 3\)[/tex], let's find [tex]\(g(-3)\)[/tex]:
[tex]\[g(-3) = (-3)^2 + 3 = 9 + 3 = 12\][/tex]
Now that we have the value of [tex]\(g(-3)\)[/tex], substitute it into the function [tex]\(f(x) = 2x - 1\)[/tex]:
[tex]\[f(g(-3)) = f(12) = 2 \times 12 - 1 = 24 - 1 = 23\][/tex]
Therefore, [tex]\(f(g(-3))\)[/tex] is equal to [tex]\(23\)[/tex].
To find the value of [tex]\( f(h(7)) \)[/tex], you need to first find [tex]\( h(7) \)[/tex] and then substitute that value into the function [tex]\( f(x) \)[/tex].
Given that [tex]\( h(x) = 2x + 1 \)[/tex], let's find [tex]\( h(7) \)[/tex]:
[tex]\[ h(7) = 2 \times 7 + 1 = 14 + 1 = 15 \][/tex]
Now that we have the value of [tex]\( h(7) \)[/tex], substitute it into the function [tex]\( f(x) = 2x^2 - 8 \)[/tex]:
[tex]\[ f(h(7)) = f(15) = 2 \times 15^2 - 8 = 2 \times 225 - 8 = 450 - 8 = 442 \][/tex]
Therefore, [tex]\( f(h(7)) \)[/tex] is equal to [tex]\( 442 \)[/tex].
The probable question may be: "Evaluate the expression f(g(-3)) using the given functions. f(x)=2x-1; g(x)= [tex]x^2[/tex]+3
a. 33
b. -77
c. 23
d. -28
Determine the value of f(h(7)) using the provided functions. f(x)= [tex]2x^2[/tex]-8; h(x)=2x+1
a. 577
b. 299
c. 450
d. 442"
