Step-by-step explanation:
We have , f(x) = 7x + 4 & g(x) = 4x-5.
A: ( f + g )( x )
We know that sum of two functions is as simple addition so,
[tex]( f + g ) (x) = f(x) + g(x)\\( f + g ) (x) = 7x+4 + 4x-5\\( f + g ) (x) = 11x - 1[/tex]
B: ( f - g ) ( x )
We know that difference of two functions is as simple subtraction so,
[tex]( f - g )(x) = f(x) - g(x)\\( f - g )(x) = 7x + 4 - ( 4x - 5 )\\( f - g )(x) = 3x + 9[/tex]
C:( fg ) (x)
We know that multiply of two functions is as simple multiplication so,
[tex]( fg) (x)= f(x).g(x)\\( fg) (x) = (7x + 4)(4x-5)\\( fg) (x) = 28x^{2} - 35x + 16x - 20\\( fg) (x) = 28x^{2} -19x -20[/tex]
D: (f/g)(x)
We know that Division of two functions is as simple division so,
[tex](\frac{f}{g})(x) = \frac{f(x)}{g(x)} \\(\frac{f}{g})(x) = \frac{7x +4}{4x-5}[/tex]
Since, both f(x) and g(x) are real valued functions , ∴ Domain of both are real numbers.
