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Let f(x)=5^(x) and g(x)=x^(2)+1. What is the value of g(f(1)-2) ?

Let f(x)=5x f(x)=5^{x} and g(x)=x2+1 g(x)=x^{2}+1 . What is the value of g(f(1)−2) g(f(1)-2) ?

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Full solution

Q. Let f(x)=5x f(x)=5^{x} and g(x)=x2+1 g(x)=x^{2}+1 . What is the value of g(f(1)−2) g(f(1)-2) ?
  1. Calculate f(1)f(1): Calculate the value of f(1)f(1).f(x)=5xf(x) = 5^{x}, so f(1)=51f(1) = 5^{1}. Calculate 515^{1}.51=55^{1} = 5.
  2. Subtract from f(1)f(1): Subtract 22 from the result of f(1)f(1). We have f(1)=5f(1) = 5 from Step 11. Now calculate f(1)−2f(1) - 2. 5−2=35 - 2 = 3.
  3. Calculate g(x)g(x): Calculate the value of g(x)g(x) when x=3x = 3.\newlineg(x)=x2+1g(x) = x^{2} + 1, so g(3)=32+1g(3) = 3^{2} + 1.\newlineCalculate 323^{2} and then add 11.\newline32=93^{2} = 9, and 9+1=109 + 1 = 10.
  4. Conclude final answer: Conclude the final answer.\newlineThe value of g(f(1)−2)g(f(1)-2) is g(3)g(3), which we calculated as 1010 in Step 33.

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