Answer:
[tex]2f\left(-3\right)+g\left(-2\right)=5[/tex]
Step-by-step explanation:
Considering the functions
As
[tex]f\left(x\right)=3x^2-1[/tex]
Putting x = -3 to determine [tex]f(-3)[/tex]
[tex]f\left(-3\right)=3\left(-1\right)^2-1[/tex]
[tex]f\left(-3\right)=3-1[/tex] ∵ [tex]\left(-1\right)^2\::\ 1[/tex]
[tex]f\left(-3\right)=2[/tex]
As
[tex]g(x)=2x+5[/tex]
Putting x = -2 to determine [tex]g(-2)[/tex]
[tex]g\left(-2\right)=2\left(-2\right)+5[/tex]
[tex]g\left(x\right)=-4+5[/tex]
[tex]g\left(x\right)=1[/tex]
So,
[tex]2f\left(-3\right)+g\left(-2\right)=2\left(2\right)+1[/tex] ∵ [tex]f\left(-3\right)=2; g\left(x\right)=1[/tex]
[tex]=4+1[/tex]
[tex]=5[/tex]
Therefore,
[tex]2f\left(-3\right)+g\left(-2\right)=5[/tex]
Keywords: combining functions, composition of functions
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