Question

If f: IR > IR, g: IR >IR are define by f(x) =4x-1and g(x) =x2+2then gof (a+1\4=

Answer 1

Answer :

gof { (a+1)/4 } ] = a² + 2

Note :

• Composition of functions : Let f : A → B and g : B → C be to 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 .

• co-dom(gof) = co-dom(g)

• dom(gof) = dom(f)

Solution :

→ Given :

• f : R → R , f(x) = 4x - 1

• g : R → R , f(x) = x² + 2

→ To find :

• gof { (a+1)/4 }= ?

Now ,

=> gof { (a+1)/4 } ] = g [ f { (a+1)/4 } ]

=> gof { (a+1)/4 } ] = g [ 4(a+1)/4 - 1 ]

=> gof { (a+1)/4 } ] = g [ a + 1 - 1 ]

=> gof { (a+1)/4 } ] = g(a)

=> gof { (a+1)/4 } ] = a² + 2

Hence ,

gof { (a+1)/4 } ] = a² + 2