Number and Algebra
Functions
Geometry and Trigonometry
Statistics and Probability
Calculus
Determine whether the function f(x)=x3f(x) = x^3f(x)=x3 with domain (−∞,∞)(-\infty,\infty)(−∞,∞) has an inverse. If it does, find the inverse.
Determine whether the natural logarithm f(x)=ln(x)f(x)=\ln(x)f(x)=ln(x) with domain (0,∞)(0,\infty)(0,∞) has an inverse. If it does, find the inverse.
Determine whether the function f(x)=x2f(x) = x^2f(x)=x2 with domain (−∞,∞)(-\infty,\infty)(−∞,∞) has an inverse. Explain your reasoning.
Determine whether the exponential function f(x)=exf(x)=e^xf(x)=ex with domain (−∞,∞)(-\infty,\infty)(−∞,∞) has an inverse. If so, find it.
Determine whether the tangent function f(x)=tan(x)f(x)=\tan(x)f(x)=tan(x) with domain (−π2,π2)(-\frac{\pi}{2},\frac{\pi}{2})(−2π,2π) has an inverse. If yes, find it.
Determine whether the function f(x)=sin(x)f(x)=\sin(x)f(x)=sin(x) with domain [−π2,π2][-\frac{\pi}{2},\frac{\pi}{2}][−2π,2π] has an inverse. If it does, state the inverse.
Determine whether the function f(x)=x2f(x) = x^2f(x)=x2 with domain (−∞,0](-\infty,0](−∞,0] has an inverse. If so, find its expression.
Determine whether the function f(x)=x2f(x) = x^2f(x)=x2 with domain [0,∞)[0,\infty)[0,∞) has an inverse. If it does, find the inverse.
Determine whether the sine function f(x)=sin(x)f(x)=\sin(x)f(x)=sin(x) with domain (−∞,∞)(-\infty,\infty)(−∞,∞) has an inverse. Justify your answer.
Determine whether the function f(x)=x2+2x+1f(x)=x^2+2x+1f(x)=x2+2x+1 restricted to domain [−1,∞)[-1,\infty)[−1,∞) has an inverse. If so, find f−1(x)f^{-1}(x)f−1(x).
Determine whether the quadratic function f(x)=x2+2x+1f(x)=x^2+2x+1f(x)=x2+2x+1 with domain (−∞,∞)(-\infty,\infty)(−∞,∞) has an inverse. Explain.
Determine whether the cubic function f(x)=x3−xf(x)=x^3-xf(x)=x3−x with domain (−∞,∞)(-\infty,\infty)(−∞,∞) has an inverse. Justify your answer.
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Question Type 6: Finding the range of more complex functions
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Question Type 8: Solving questions with the values of inverses