If f(x) = 2x and g(x) = 2x² - 1, find f(g(3))

Understand the Problem

The question requires us to evaluate the composite function f(g(3)). We need to first determine the value of g(3) using the function g(x) = 2x² - 1, and then substitute that result into the function f(x) = 2x.

Answer

The answer is $34$.

Steps to Solve

Calculate g(3)

To find ( g(3) ), we substitute ( x = 3 ) into the function ( g(x) = 2x^2 - 1 ).

[ g(3) = 2(3)^2 - 1 = 2(9) - 1 = 18 - 1 = 17 ]

Calculate f(g(3))

Now that we have found ( g(3) = 17 ), we use this value to find ( f(g(3)) ) by substituting ( x = 17 ) into the function ( f(x) = 2x ).

[ f(g(3)) = f(17) = 2(17) = 34 ]

The final answer is ( 34 ).

More Information

The value obtained, 34, represents the result of evaluating the composite function ( f(g(3)) ). Composite functions are a key part of understanding function relationships and mappings in mathematics.

Tips

Forgetting parentheses: It's important to correctly apply function values. Remember that ( g(3) ) must be calculated before substituting into ( f ).
Arithmetic Errors: Be careful while performing arithmetic operations, like multiplication or subtraction; double-check to avoid simple mistakes.

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