Consider the following function on the given domain. q(x)=(x-5)^(4)+1,x >= 5

Understand function and domain: Understand the function and its domain. The function q(x) = (x-5)^(4) + 1 is defined for x >= 5. This means that the smallest value x can take is 5, and there is no upper limit to the values of x. Since the function involves raising (x-5) to the fourth power, the output will always be positive or zero (when x=5), and then 1 is added, making the minimum output value 1. Therefore, the range of q(x) is [1, ∞).Determine inverse function domain: Determine the domain of the inverse function. The domain of the inverse function q^(-1)(x) is the range of the original function q(x). Since we have established that the range of q(x) is [1, ∞), the domain of q^(-1)(x) will be the same.

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Consider the following function on the given domain.
q(x)=(x-5)^(4)+1,x >= 5

Consider the following function on the given domain. $\newline$ $q(x)=(x-5)^{4}+1, x \geq 5$

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Grade 7

One-step inequalities: word problems

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Q. Consider the following function on the given domain.

\newline

q(x)=(x-5)^{4}+1, x \geq 5

Understand function and domain: Understand the function and its domain. $\newline$ The function $q(x) = (x-5)^{4} + 1$ is defined for $x \geq 5$ . This means that the smallest value $x$ can take is $5$ , and there is no upper limit to the values of $x$ . Since the function involves raising $(x-5)$ to the fourth power, the output will always be positive or zero (when $x=5$ ), and then $1$ is added, making the minimum output value $1$ . Therefore, the range of $q(x)$ is $x \geq 5$ $0$ .
Determine inverse function domain: Determine the domain of the inverse function. $\newline$ The domain of the inverse function $q^{-1}(x)$ is the range of the original function $q(x)$ . Since we have established that the range of $q(x)$ is $[1, \infty)$ , the domain of $q^{-1}(x)$ will be the same.