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Composition of functions

Solve the first problem 18 problems

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  1. Evaluating a function by substitution ●○○○○ 10 ptsIf g(2x−5)=3x+9g(2x - 5) = 3x + 9 for all real xx, find g(1)g(1).
  2. Evaluating a function from its composite form ●○○○○ 10 ptsLet g(2x+5)=4x2−3x+2g(2x + 5) = 4x^2 - 3x + 2. Find g(−3)g(-3).
  3. Composition of two functions at points ●○○○○ 10 ptsIf f(x)=x2−2x+1f(x) = x^2-2x+1 and g(x)=2x+1g(x) = \sqrt{2x+1}, what is the value of f(g(4))−g(f(3))f(g(4)) - g(f(3))?
  4. Evaluate a function from two values ●●○○○ 20 ptsIf f(1)=5f(1)=5, f(2)=8f(2)=8 and f(x)=ax+bx+2f(x)=ax+bx+2, what is the value of f(3)f(3)?
  5. Function value via substitution ●●○○○ 20 ptsGiven the function f(x−1)=x2−2xf(x-1)=x^{2}-2x, find the value of f(2)f(\sqrt{2}).
  6. Input value of a linear function ●●○○○ 20 ptsGiven that f(x2−1)=2x+3f\left(\frac{x}{2} - 1\right) = 2x + 3 for all xx, and f(m)=6f(m) = 6, find the value of mm. Give your answer as a decimal.

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