Does the function $$f(x) = x^3 + 1$$ have an inverse?

No, because it is not defined for all $$x$$ .

Given the table below, does the function have an inverse? | $$x$$ | $$1$$ | $$2$$ | $$3$$ | $$4$$ | |-----|-----|-----|-----|-----| | $$f(x)$$ | $$5$$ | $$7$$ | $$9$$ | $$11$$ |

Yes, because each $$x$$ maps to a unique $$f(x)$$ .

No, because $$f(x)$$ repeats values.

Yes, because $$f(x)$$ is always increasing.

No, because $$x$$ repeats values.

Which of the following is true about the relationship between $$f(x) = 2^x$$ and $$g(x) = \log_2 x$$ ?

$$g(x)$$ is the inverse of $$f(x)$$ .

$$f(x)$$ is the inverse of $$g(x)$$ .

$$f(x)$$ and $$g(x)$$ are the same function.

$$f(x)$$ and $$g(x)$$ are unrelated.

Given $$f(x) = 2x + 1$$ , does $$f$$ have an inverse?

No, because it is not defined for all $$x$$ .

Which of the following statements is true about logarithmic and exponential functions?

A logarithmic function is the inverse of an exponential function.

An exponential function is the inverse of a quadratic function.

A logarithmic function is the inverse of a linear function.

An exponential function is the inverse of a cubic function.

Does the function $$f(x) = x^2$$ have an inverse for all real numbers?

No, because it is not one-to-one over all real numbers.

No, because it is not defined for all $$x$$ .

col alg f 3 test

Authored by LIZ SMITH

Mathematics

12th Grade

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Yes, because it is one-to-one.

No, because it is not one-to-one.

Yes, because it is even.

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