For given functions f(x) and g(x) the composite function f(g(x)) is \(f(g(x))=4x^4+22x^2+32\)
What is function?
- "It defines a relation between input values and output values."
- "In function, for each input there is exactly one output."
What is composition of function?
- "It is applying one function to the results of another."
- "It is written is \(\( f\circ g(x)=f(g(x))\) "
- "First apply function f, then apply function g on the result of function f "
For given question,
We have been given two functions,
\(f(x) = x^2 + x + 2,~g(x) = 2x^2 + 5.\)
We need to find f(g(x))
This means we need to find composite function \(\( f\circ g(x)=f(g(x))\)
We have, \(g(x) = 2x^2 + 5\)
We find the value of f(x) for x = g(x)
\(f(g(x))\\\\=f(2x^2 + 5)\\\\=(2x^2 + 5)^2 + (2x^2 + 5) + 2\\\\=[(2x^2)^2+2(2x^2)(5)+5^2]+2x^2+5+2\\\\=[4x^4+20x^2+25]+2x^2+7\\\\=4x^4+20x^2+2x^2+25+7\\\\=4x^4+22x^2+32\)
Therefore, for given functions f(x) and g(x) the composite function f(g(x)) is \(f(g(x))=4x^4+22x^2+32\)
Learn more about composite function here:
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