Answer: f(x) = 4x and g(x) = 3x
Step-by-step explanation:
[tex]\text{ If }f(x) = 3 - 4x \text{ and } g(x) = 16x-3[/tex]
[tex]\implies (fog)(x) = f[g(x)] = f(16x-3) = 3-4(16x-3)=3-64x+12=15-64x\neq 12x[/tex]
[tex]\text{ If } f(x) = 6x^2 \text{ and }g(x) =\frac{2}{x}[/tex]
[tex]\implies (fog)(x) = f[g(x)] = f(\frac{2}{x}) = 6(\frac{2}{x})^2=\frac{24}{x^2}\neq 12x[/tex]
[tex]\text{ If } f(x) = \sqrt{x}\text{ and } g(x) = 144x[/tex]
[tex]\implies (fog)(x) = f[g(x)] = f(144x) = \sqrt{144x}=12\sqrt{x}\neq 12x[/tex]
[tex]\text{ If }f(x) = 4x \text{ and } g(x) = 3x[/tex]
[tex]\implies (fog)(x) = f[g(x)] = f(3x) = 4(3x)=12x=12x[/tex]
Hence, Fourth pair of function f(x) and g(x) is giving (fog)=12x.
