# You did letter B for me, can you check my work?

if f(x)=lnx, g(x)=e^3x, and h(x)=x^4 find following

A)(f of g)(x)and the domain of f of g

B) (g of f)(x) and the domain of g of f

C) (f of h)(x) and the domain of f of h

A) f(g(x))
=lnx(e^3x)
domain x>0

C)f(h(x))
=lnx(x^4)
x>4

1. 👍
2. 👎
3. 👁
1. A) close , but not quite

f(g(x))
= f(e^3x)
= ln (e^(3x)) , you have an extra x in there

f(x) was defined as lnx, so whatever x is replaced by on the left side, must be replaced by on the right side ....e.g.
f(2) = ln2
f(happy face) = ln(happy face)
f(e^3x) = ln(e^3x)

C) you made the same error

f(h(x)) = f(x^4) = ln x^4

the domain would be x > 0

1. 👍
2. 👎
2. i understand now thank you

1. 👍
2. 👎

## Similar Questions

1. ### alebra

Let f(x)=2x^2+x-3 and g(x)=x-1. Perform the indicated operation then find the domain. (f*g)(x) a.2x^3-x^2-4x+3; domain:all real numbers b.2x^3+x^2-3x; domain: all real numbers c.2x^3+x^2+4x-3; domain: negative real numbers

2. ### MATH

for the given functions f and g find the following and state the domain of each result f(x)=3x+1/8x-9; g(x)=5x/8x-9 A) (f+g)(x)=? B)domain of (f+g) c) (f/g)(x)=? d) domain of f/g? please show work

3. ### math

Find the rules for (f∘g)(x) and (g∘f)(x) and give the domain of each composite function. f(x) = x^2 g(x) = √(1-x) The Domain of (f∘g)(x) is : (f∘g)(x) = The Domain of (g∘f)(x) is : (g∘f)(x) =

4. ### College Algebra

Consider the function f(x)=4 - x^2 for the domain [ 0,∞). Find f^−1 (x), where f^−1 is the inverse of f. Also state the domain of f^−1 in interval notation. f^-1 (x) = ___ for the domain ___

1. ### Calculus

Evaluate the function below from x = 1 up to x = 4. ∫(7−lnx(x)(3+lnx))dx

2. ### math

If y = u+ 2e^u and u = 1+lnx, find dy/dx when x= (1/e) ?

3. ### Calculus check and help

Let R be the region bounded by the curves y=lnx^2 and y=x^2-4 to the right of the y-axis. A. Find the area of R. B. Find the folume geneated when R is rotated about the line y=-4. C. Write, but do not evaluate the integral

4. ### Calculus

Evaluate the definite integral. dx/(x*sqrt(lnx)) from 1 to e^4 I'm having trouble figuring this out, I might be overthinking it. The way I've approached this is by using u substitution and letting u=lnx. I keep getting the wrong

1. ### college alg

for the given functions f and g find the following and state the domain of each result f(x)=3x+1/8x-9; g(x)=5x/8x-9 (they look like fractions) A) (f+g)(x)=? B)domain of (f+g) c) (f/g)(x)=? d) domain of f/g? please show work

2. ### Calc

Find the functions a) f o g, b) g o f, c) f o f, d) g o g, and their domains. f(x)= square root of x, g(x)= cube root of 1-x These are my answers, but I am not sure about them and I only figured out one domain... that is the part

3. ### Math

1) Let f(x)=9x-2;g(x)=under square root 3x+7. Find each of the following. A) domain of (f+g) B) domain of fg C) domain of f/g (my answer is all r real number am i right?) 2) Let f(x)=3x-2;g(x)=5x+1. Compute the indicated value. A)