Function Substitution Math Practice Problems

Here you will find a concise collection of function substitution math practice problems. Visit this page directly at hunkim.com/functionsubstitution

1. f(x)=x^2. g(x)=2f(x). Actual equation of g(x)?
   Solution
   g(x)=2x^2
   
   
2. f(x)=3x^2-2x. g(x)=f(x+1). Actual equation of g(x)?
   Solution
   g(x)=3(x+1)^2-2(x+1) or 3x^2+4x+1
   
   
3. f(x)=3x+1. g(x)=-f(x). Actual equation of f(x)?
   Solution
   -3x-1
   
   
4. f(x)=\frac{1}{2}x^2-x. g(x)=f(-x). Actual equation of g(x)?
   Solution
   \frac{1}{2}x^2+x
   
   
5. f(x)=1-2x. g(x)=2f(3x)+1. Actual equation of g(x)?
   Solution
   g(x)=-12x+3
   
   
6. f(x)=2x^2-3x+1. g(x)=-2f(2x-6)+3. Actual equation of g(x)?
   Solution
   -16x^2+108x-179
   
   
7. f(x)=\log_2 (x+2)-\frac{3^x}{e^{\sin x}}. g(x)=f(x-5). Actual equation of g(x)?
   Solution
   g(x)=\log_2(x-3)-\frac{3^{x-5}}{e^{\sin(x-5)}}
   
   
8. h(t)=3t^2-t+1. g(t)=-2h(1-3t)-h(2t)+5. Actual equation of g(t)?
   Solution
   -66t^2+32t-2
   
   
9. f(x)=x^2. g(x)=\frac{ f(x+h)-f(x) }{ (x+h)-x }. Actual equation of g(x)?
   Solution
   2x+h

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