If f(x)=-3x+4 and g(x)=x2, then find g○f(-2).
Answers
Answer :
gof(-2) = 100
Note :
• Composition of functions :
Let f : A → B and g : B → C be two given functions , then the composition of f and g is a function defined from A to C .
• It is denoted by gof and given by ;
(gof)(x) = g{f(x)} , for all x € A .
• Thus , co-dom.(gof) = co-dom.(g) and dom.(gof) = dom.(f)
• The composition of two functions is also called the resultant of the two functions or the function of functions .
• gof is said to be well defined if ;
range(f) ⊆ domain(g) .
Solution :
- Given : f(x) = -3x + 4 ; g(x) = x²
- To find : gof(-2) = ?
We know that ,
gof(x) = g{f(x)}
Thus ,
=> gof(x) = g{f(x)}
=> gof(x) = g{-3x + 4}
=> gof(x) = {-3x + 4}²
=> gof(x) = (-3x)² - 2•3x•4 + 4²
=> gof(x) = 9x² - 24x + 16
Thus ,
• gof(x) = {-3x + 4}² or 9x² - 24x + 16
Now ,
=> gof(-2) = {-3•(-2) + 4}²
=> gof(-2) = {6 + 4}²
=> gof(-2) = 10²
=> gof(-2) = 100