Home > Precalculus > Function Composition

If #h(x)=(f+g)(x), f(x)=5x+2# how do you determine g(x) given #h(x)=sqrt(x+7)+5x+2#?

Answer 1

Ariana Alvarez

#g(x)=sqrt(x+7)#

#"note that "(f+g)(x)=f(x)+g(x)#

#h(x)=f(x)+g(x)" then"#

#g(x)=h(x)-f(x)#

#color(white)(xxx)=sqrt(x+7)+5x+2-5x-2=sqrt(x+7)#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Elias Ackerman

To determine ( g(x) ) given ( h(x) = \sqrt{x + 7} + 5x + 2 ) and ( f(x) = 5x + 2 ), subtract ( f(x) ) from ( h(x) ) to find ( g(x) ):

[ g(x) = h(x) - f(x) ]

[ g(x) = (\sqrt{x + 7} + 5x + 2) - (5x + 2) ]

[ g(x) = \sqrt{x + 7} ]

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.