Question

Please give an example of another function whose inverse is only defined if we restrict the domain of the original function.

(In general, a function must be one-to-one in order to have an inverse function. Some functions, though, have inverses that are very useful but require us to restrict the original function to an interval where it IS one-to-one. This is the case with all of our trigonometric functions.)

Answer 1

OH NANANA

Explanation:

Find all real numbers $x$ such that $3x - 7 \le 5x +9$. Give your answer as an interval.Find all real numbers $x$ such that $3x - 7 \le 5x +9$. Give your answer as an interval.Find all real numbers $x$ such that $3x - 7 \le 5x +9$. Give your answer as an interval.Find all real numbers $x$ such that $3x - 7 \le 5x +9$. Give your answer as an interval.Find all real numbers $x$ such that $3x - 7 \le 5x +9$. Give your answer as an interval.Find all real numbers $x$ such that $3x - 7 \le 5x +9$. Give your answer as an interval.Find all real numbers $x$ such that $3x - 7 \le 5x +9$. Give your answer as an interval.Find all real numbers $x$ such that $3x - 7 \le 5x +9$. Give your answer as an interval.

Answer 2

f(x) = x^2

Explanation:

The square root function is defined to have a non-negative range only. That corresponds to restricting the domain of f(x) = x^2 to positive values of x.

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The attached graph shows the domain-restricted f(x)=x² in solid red and the corresponding f⁻¹(x) = √x in solid blue. The other halves of those curves are shown as dotted lines (and are inverse functions of each other, too). The dashed orange line is the line of reflection between a function and its inverse.