Given f(x)=x^2+2x+3 and g(x)=x+4/3 solve for f(g(x)) when x=2

Step-by-step explanation:

We are provided with the following functions:

f(x) = x² + 2x + 3

The given problem also requires to find the Composition of Functions, f(g(x)) when x = 2.

The Composition of Function f with function g can be expressed as ( f ° g )(x) = f(g(x)).  In solving for the composition of functions, we must first evaluate the innermost function, g(x), then use the output as an input for f(x).

Starting with g(x), we will use x = 2 as an input value into the function:

Transform the first term, x = 2, into a fraction with a denominator of 3 to combine with 4/3:

Next, we will use   as input for the function, f(x) = x² + 2x + 3:

f(x) = x² + 2x + 3

Use the Quotient-to-Power Rule of Exponents onto the leading term (x²):

Multiply the numerator (10) of the middle term by 2:

Finally, add the three fractions on the right-hand side of the equation:

Keywords:

Composition of functions

f o g

f (g(x))

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Learn more about Composition of Functions here:

linear pair postulates