Exercise 26Which of the following functions areone-to-one? Justify your answers.(a)f(x) =x3+ 1(b)f(x) =x(x−2) + 1(c)f(x) =x3−x(d)f(x) =ax2, wherea= 0Exercise 27Find the inverse of each of the followingfunctions.(a)f(x) =(1−x)3(b)f(x) = 5−1x(c)f(x) =15−xExercise 28For each of the following functionsf, find theinverse functionf−1, and sketch the graphoff−1.(a)f(x) = 2−3x(b)f(x) = 2x+ 2(x∈(−1,2))Exercise 29Consider the functionf(x) =x2−4x+ 7.(a) Complete the square in the rule off.(b) Sketch the graph off.(c) Using your sketch, specify a one-to-onefunctiongthat is a restriction offandhas the same image set asf.(d) Find the inverse functiong−1ofg.Pair each exponential function below with itsapproximately equivalent form. (Try to dothis without using a calculator.)(a)f(x) = 1000x(b)f(x) = 0.5x(c)f(x) =e6.907 755x(d)f(x) = 2.718 282x(e)f(x) =e−0.693 147x(f)f(x) =exExercise 31Find the exact value of each of the followingexpressions, without using your calculator.(a) log31(b) log5(125)(c) ln(e3.1)(d) log10(√1000)(e)eln 4(f) 23 log25Exercise 32For each of the following equations, find thevalue ofxthat satisfies it, if there is such avalue.(a) 3 = log5x(b)x= log√2(−2)(c)12= logx9(d)x= log−112Exercise 33Find the exact value of the expressioneln 2+ log51125+ ln(4e)−ln 4,without using your calculator.Exercise 34For each of the following functions, describehow you could obtain its graph by applyingscalings and translations to the graph of thefunctionf(x) =ex, and sketch the graph ofthe function.(a)g(x) =ex−1+ 1(b)h(x) =ex/24 Exponentials andlogarithmsExercise 306