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Sum

Find the domain and range of the following real function:

f(x) = `sqrt(9 - x^2)`

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#### Solution

f(x) = `sqrt(9 - x^2)`

Since `sqrt(9 - x^2)` is defined for all real numbers that are greater than or equal to –3 and less than or equal to 3, the domain of *f*(*x*) is {*x* : –3 ≤ *x* ≤ 3} or [–3, 3].

For any value of *x* such that –3 ≤ *x* ≤ 3, the value of *f*(*x*) will lie between 0 and 3.

∴The range of *f*(*x*) is {*x*: 0 ≤ *x* ≤ 3} or [0, 3].

Concept: Some Functions and Their Graphs

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