Question

for which pair of functions is (gof)(a)=|a|-2?

-f(a)=a^2-4 and g(a)= square root of a
-f(a)=1/2a-1 and g(a)=2a-2
-f(a)=5+a^2 and g(a)= square root of a-5-2
-f(a)=3-3a and g(a)=4a-5

Answer 1

Answer:

-f(a)=1/2a-1 and g(a)=2a-2

Step-by-step explanation:

Answer 2

The pair of functions (gof)(a) = |a| - 2 is ${data-answer}amp;f(a)=5+a^{2}, g(a)=\sqrt{a-5}-2$ .

How to solve the pair of functions?

The pair of functions is (gof)(a) = |a| - 2

1. ${data-answer}amp;f(a)=a^{2}-4, g(a)=\sqrt{a}$

${data-answer}amp;g o f(a)=g\left(a^{2}-4\right)$

${data-answer}amp;=\sqrt{a^{2}-4} \neq|a|-2$

2. ${data-answer}amp;f(a)=\frac{1}{2 \cdot a-1}, g(a)=2 \cdot a-2$

${data-answer}amp;g \circ f(a)=g\left(\frac{1}{2 \cdot a-1}\right)$

${data-answer}amp;=\frac{2}{2 \cdot a-1}-2$

${data-answer}amp;=\frac{1-2 \cdot a}{2 \cdot a-1} \neq|a|-2$

3. ${data-answer}amp;f(a)=5+a^{2}, g(a)=\sqrt{a-5}-2$

${data-answer}amp;g o f(a)=g\left(5+a^{2}\right)$

${data-answer}amp;=\sqrt{5+a^{2}-5}-2$

${data-answer}amp;=\sqrt{a^{2}}-2$

${data-answer}amp;=|a|-2$

4. ${data-answer}amp;f(a)=3-3 \cdot a, g(a)=4 \cdot a-5$

${data-answer}amp;g o f(a)=g(3-3 \cdot a)$

${data-answer}amp;=4(3-3 \cdot a)-5$

${data-answer}amp;=7-12 \cdot a \neq|a|-2$

The pair of functions (gof)(a) = |a| - 2 is

${data-answer}amp;f(a)=5+a^{2}, g(a)=\sqrt{a-5}-2$ .

Therefore, the correct answer is option C. ${data-answer}amp;f(a)=5+a^{2}, g(a)=\sqrt{a-5}-2$.

To learn more about the pair of functions

https://brainly.com/question/9170205

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