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Let f(x)=7-sqrt(x^(2)+1) and g(x)=x-4 . Then (f@g)(2)= (f@g)(x)=

Question

Let f(x)=7-sqrt(x^(2)+1) and g(x)=x-4 . Then (f@g)(2)= (f@g)(x)=

Let f(x)=7-sqrt(x^(2)+1) and g(x)=x-4 . Then (f@g)(2)= (f@g)(x)=

Solution

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AprilMaster · Tutor for 5 years

Answer

<p> 1. \( 7 - \sqrt{5} \) 2. \( 7 - \sqrt{1 + (-4 + x)^2} \)</p>

Explain

<p> <br />1. The composition of functions \( f \) and \( g \) is given by \( (f \circ g)(x) = f(g(x)) \). <br />2. For \( (f \circ g)(2) \), we substitute \( x = 2 \) into \( g(x) \) to get \( g(2) \). Then, we substitute this result into \( f(x) \) to get \( f(g(2)) \). <br />3. For \( (f \circ g)(x) \), we substitute \( g(x) \) into \( f(x) \) to get the expression for \( (f \circ g)(x) \).<br /></p>
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