The value of (f · g)(x) is 4√x + 1 and (g · f)(x) is [tex]\sqrt{4x+1}[/tex]
What is Combination of Function ?
The domain of an arithmetic combination of functions f and g consists of all real numbers that are common to the domains of f and g.
Given expression,
f(x) = 4x + 1
g(x) = √x
Now, find (f · g)(x)
(f · g)(x) = f( g(x) )
Next, insert the value of g(x) in f(x) value by replacing x value in f(x)
(f · g)(x) = 4 ( √x ) + 1
= 4√x + 1
Next, find (g · f)(x)
(g · f)(x) = g( f(x) )
Now, insert the value of f(x) in g(x) value by replacing x value in g(x)
(g · f)(x) = √4x + 1
= [tex]\sqrt{4x+1}[/tex]
Hence, the value of (f · g)(x) is 4√x + 1 and (g · f)(x) is [tex]\sqrt{4x+1}[/tex]
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