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Chapter 1: Problem 25

Evaluate (if possible) the function at each specified value of the independent variable and simplify. \(f(y)=3-\sqrt{y}\) (a) \(f(4)\) (b) \(f(0.25)\) (c) \(f\left(4 x^{2}\right)\)

Short Answer

Expert verified
The evaluated function results are: (a) \(f(4) = 1\), (b) \(f(0.25) = 2.5\), and (c) \(f(4x^{2}) = 3-2x\).

Step by step solution

01

Evaluate the function at \(y = 4\)

To evaluate the function at \(y = 4\), substitute \(y = 4\) in the given function \(f(y)\). The function becomes \(f(4) = 3 - \sqrt{4}\). Simplify \(\sqrt{4}\) to 2. Then subtract from 3 to get \(f(4) = 1\).
02

Evaluate the function at \(y = 0.25\)

To evaluate the function at \(y = 0.25\), substitute \(y = 0.25\) in the given function \(f(y)\). The function becomes \(f(0.25) = 3 - \sqrt{0.25}\). Simplify \(\sqrt{0.25}\) to 0.5. Then subtract from 3 to get \(f(0.25) = 2.5\).
03

Evaluate the function at \(y = 4x^{2}\)

To evaluate the function at \(y = 4x^{2}\), substitute \(y = 4x^{2}\) in the given function \(f(y)\). The function becomes \(f(4x^{2})=3-\sqrt{4x^{2}}\). Simplify \(\sqrt{4x^{2}}\) to \(2x\). Then subtract from 3 to get \(f(4x^{2})=3-2x\).

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