Question

Let F(x)=etand g(x) = x+6. What are the domain and range of (gºf)(x)?O domain: x > 0range: y>O domain: x>6range:y> 0O domain: all real numbersrange:y> 6O domain: all real numbersrange: all real numbers

Answer 1

`f(x)=e^x`
`g(x)=x+6`

then the compound function (gºf)(x) is:

`(g\circ f)(x)=g(f(x))=g(e^x)=e^x+6`

then the domain would be all the real numbers, because it is the domain of the exponential function.

Remember that the range of the exponential funtion is y>0 but in the compound we are moving upward the original function 6 units in the y-axis, then the range would be y>6

so the final answer is C