Find q(r(x)) q(x)=x^2+6 , r(x) = square root of x+1

Problem

q(r(x)),q(x)=x2+6,r(x)=√(,x+1)

Solution

1. Identify the outer function q(x)=x2+6 and the inner function r(x)=√(,x+1)

2. Substitute the expression for r(x) into every instance of x in the function q(x)

q*(r(x))=(√(,x+1))2+6

3. Simplify the expression by squaring the square root, noting that (√(,a))2=a

q*(r(x))=x+1+6

4. Combine the constant terms to reach the final simplified form.

q*(r(x))=x+7

Final Answer

q*(r(x))=x+7

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