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Let 
f(x)=(3)/(4)x+10 and 
g(x)=x^(2)-3. What is the value of 
f(-2-g(3)) ?

Let f(x)=34x+10 f(x)=\frac{3}{4} x+10 and g(x)=x23 g(x)=x^{2}-3 . What is the value of f(2g(3)) f(-2-g(3)) ?

Full solution

Q. Let f(x)=34x+10 f(x)=\frac{3}{4} x+10 and g(x)=x23 g(x)=x^{2}-3 . What is the value of f(2g(3)) f(-2-g(3)) ?
  1. Given Functions: We are given two functions:\newlinef(x)=34x+10f(x) = \frac{3}{4}x + 10\newlineg(x)=x23g(x) = x^2 - 3\newlineWe need to find the value of f(2g(3))f(-2 - g(3)).\newlineFirst, we will calculate g(3)g(3).\newlineSubstitute x=3x = 3 into g(x)g(x).\newlineg(3)=323g(3) = 3^2 - 3
  2. Calculate g(3)g(3): Calculate the value of g(3)g(3).
    g(3)=323g(3) = 3^2 - 3
    g(3)=93g(3) = 9 - 3
    g(3)=6g(3) = 6
    Now we have the value of g(3)g(3).
  3. Substitute g(3)g(3): Next, we will substitute g(3)g(3) into the expression 2g(3)-2 - g(3).\newline2g(3)=26-2 - g(3) = -2 - 6
  4. Calculate 2g(3)-2 - g(3): Calculate the value of 2g(3)-2 - g(3).
    2g(3)=26-2 - g(3) = -2 - 6
    2g(3)=8-2 - g(3) = -8
    Now we have the value of 2g(3)-2 - g(3).
  5. Substitute 8-8 into f(x)f(x): Finally, we will substitute 8-8 into f(x)f(x) to find f(2g(3))f(-2 - g(3)).\newlinef(8)=(34)(8)+10f(-8) = (\frac{3}{4})(-8) + 10
  6. Calculate f(8)f(-8): Calculate the value of f(8)f(-8).
    f(8)=34(8)+10f(-8) = \frac{3}{4}(-8) + 10
    f(8)=6+10f(-8) = -6 + 10
    f(8)=4f(-8) = 4
    Now we have the value of f(2g(3))f(-2 - g(3)).

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