Learn Intro to Composing Functions & fg x, practice Composition of Functions Example.
Let us say, we have two functions 'f' and 'g' ,then we can make new functions from these by suitable combinations. Four such combinations are
(1) \(f + g \) (3) \(f g \)
(2) \(f - g \) (4) \(\dfrac {f}{g }\)
The definition is similar to the way we define addition, subtraction, division & multiplication in real numbers.
So
\((f + g) (x) = f(x) + g(x) \) \( fg(x) = f(x)\; g(x)\)
\((f – g) (x) = f(x) – g(x)\) \(\Big(\dfrac {f}{g}\Big)(x) = \Large \frac {f(x)}{g(x)}\)
A \(x^2 + 8x\)
B \(7x^2 + 9x - 10\)
C \(x^2 + 6x - 1\)
D \(x^2 + x\)
A \(\dfrac {5}{8}\)
B \(\dfrac {-8}{5}\)
C \(\dfrac {7}{3}\)
D \(\dfrac {-3}{7}\)
A 0
B 7
C 8
D –2
\((fg)\,(1)=f(1)\,g(1)\) (by definition)
\(=\sqrt {2-1}×\sqrt {1^2-1}\)
\(=\sqrt 1 ×\sqrt {1-1}\)
\(=\sqrt 1 ×\sqrt {0}\)
\(=1×0=0\)
Option A is Correct
A \(\sqrt {3x+5}\,(x^2+2)\)
B \((2x^2+7)\;\sqrt {2+x}\)
C \(\dfrac {3+x^2}{x}\)
D \(\dfrac {x+7}{9}\)
\(h(x)=\dfrac {f}{g}(x)=\dfrac {f(x)}{g(x)}\rightarrow\) by definition
\((f \,/g)(\alpha)=f(\alpha)/g(\alpha)\)
so find \( f(\alpha)\) and \(g(\alpha)\) separately and obtain the division.
A \(\dfrac {5x+3}{x+7}\)
B \(\dfrac {2x^2+3x+1}{x+2}\)
C \(\dfrac {x-2}{x^2+1}\)
D \(\dfrac {\sqrt {x+3}}{x+6}\)
