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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)=x2−3 g(x)=x^{2}-3 . What is the value of f(−2−g(3)) f(-2-g(3)) ?

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Full solution

Q. Let f(x)=34x+10 f(x)=\frac{3}{4} x+10 and g(x)=x2−3 g(x)=x^{2}-3 . What is the value of f(−2−g(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)=x2−3g(x) = x^2 - 3\newlineWe need to find the value of f(−2−g(3))f(-2 - g(3)).\newlineFirst, we will calculate g(3)g(3).\newlineSubstitute x=3x = 3 into g(x)g(x).\newlineg(3)=32−3g(3) = 3^2 - 3
  2. Calculate g(3)g(3): Calculate the value of g(3)g(3).
    g(3)=32−3g(3) = 3^2 - 3
    g(3)=9−3g(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 −2−g(3)-2 - g(3).\newline−2−g(3)=−2−6-2 - g(3) = -2 - 6
  4. Calculate −2−g(3)-2 - g(3): Calculate the value of −2−g(3)-2 - g(3).
    −2−g(3)=−2−6-2 - g(3) = -2 - 6
    −2−g(3)=−8-2 - g(3) = -8
    Now we have the value of −2−g(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(−2−g(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(−2−g(3))f(-2 - g(3)).

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