solve equation

Question

please help solve

 

if  f(x) = 2x + 4, and g(x) = (x^2 + x + 5), find g (f(x).

 

 

 

solve y = 3^x

Answer 1

If f(x) = 2x + 4, and g(x) = (x^2 + x + 5), find g (f(x)).

 

g(f(x)) refers to the composition of g and f. 

 

To find g(f(x)), simply replace the x in g(x) with f(x)

 

 g(x) = x² + x + 5

 

g(f(x)) = f(x)² + f(x) + 5                          (Replace x with f(x))

 

g(f(x)) = (2x+4)² + (2x+4) + 5                (f(x)=2x+4)

 

g(f(x)) = 4x² + 16x + 16 + 2x + 4 + 5      (Multiply out)

 

g(f(x)) = 4x² + 18 x + 25                         (Combine like terms)

 

Solve y = 3^x     (Solve for x?)

 

log₃(y) = log₃(3^x) = x