Name: Calculus IB Homework If f(x)=√(x-4) ,g(x)=x^2, then find the compositions fog,gof,fof and gog. Also, state the domain of the resulting composite function. fog(x)= gof(x)= fof(x)= gog(x)= Graph the following composite function. f(x)= {█(x+1 , x<0@2 , x=0@x^2 , x>0)┤ Find the inverse of the function and write it in the form y=f^(-1) (x). Verify the relationships f(f^(-1) (x))=x or f^(-1) (f(x))=x. f(x)=7x/(2x-3) Solve the following equations without using a calculator. Reduce expressions, if necessary, to natural logarithms. (x+3)^(4⁄3)=16 9^x+3^(x+1)-18=0 log_3⁡(x-5) + log_3⁡〖(x+3)=2〗 Solve the following trigonometric equations. 9〖 tan〗^2 x-3=0 〖sin〗^2 x-2 cosx-2=0 Type equation here. Evaluate the following limits. lim┬(x→-2)⁡(x^2+5x+7) lim┬(x→3)⁡〖(-5x)/√(4x-3)〗 Evaluate the following limits. lim┬(x→1)⁡〖(x^2-7x+6)/(x-1)〗 lim┬(x→5)⁡〖(√(x+4) -3)/(x-5)〗 Evaluate the following limits. lim┬(x→3^+ )⁡〖5/(x-3)〗 lim┬(x→5^- )⁡〖3/(x-5)^5 〗 Evaluate the following limits. lim┬(x→+∞)⁡〖(4x^2-7)/(8x^2+5x+2)〗 lim┬(x→+∞)⁡〖(2x+1)/(3x^4-2)〗 Prove algebraically that the following function is one-to-one. f(x)= √(x-3)

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Calculus IB                  Homework

1. If , then find the compositions Also, state the domain of the resulting composite function.

2. Graph the following composite function.

3. Find the inverse of the function and write it in the form   Verify the relationships  or

4. Solve the following equations without using a calculator. Reduce expressions, if necessary, to natural logarithms.

1. +

5. Solve the following trigonometric equations.

6. Evaluate the following limits.

7. Evaluate the following limits.

8. Evaluate the following limits.

9. Evaluate the following limits.

10. Prove algebraically that the following function is one-to-one.