1. Consider the functions f(x) = 100+22r and g(x) = x. (a) Find f(g(x)) and g(f(x))....

 

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1. Consider the functions f(x) = 100+22r and g(x) = x³. (a) Find f(g(x)) and g(f(x)). (b) Find the inverse of f(x) and g(x). (c) Find the derivative of f(g(r)) with respect to r. (Hint: put g(x) = y; then use the chain rule.) (d) Find the derivative of g(f(x)) with respect to a. (Hint: put f(x) = z; then use the chain rule.) 2. Find the derivatives of the following functions. (Hint: Use the chain rule.) (a) f(x) = 5x (b) f(x) = (x²-3x)ef (c) f(x) = 2x² (Hint: Take In of both sides and differentiate implicitly) (d) f(x) = 3. Answer the following questions (don't use a calculator; your final answer can have numbers or In functions). (a) eln 40 ? (b) logo.2(z) = ? (c) log,(x)=? (d) In(ab) = ? (e) In(1) =? (f) log101 1=? 1. Consider the functions f(x) = 100+22r and g(x) = x³. (a) Find f(g(x)) and g(f(x)). (b) Find the inverse of f(x) and g(x). (c) Find the derivative of f(g(r)) with respect to r. (Hint: put g(x) = y; then use the chain rule.) (d) Find the derivative of g(f(x)) with respect to a. (Hint: put f(x) = z; then use the chain rule.) 2. Find the derivatives of the following functions. (Hint: Use the chain rule.) (a) f(x) = 5x (b) f(x) = (x²-3x)ef (c) f(x) = 2x² (Hint: Take In of both sides and differentiate implicitly) (d) f(x) = 3. Answer the following questions (don't use a calculator; your final answer can have numbers or In functions). (a) eln 40 ? (b) logo.2(z) = ? (c) log,(x)=? (d) In(ab) = ? (e) In(1) =? (f) log101 1=?