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) (fogof)(2) i don't get the answer.please help me. Thanks
3427648
Thank you
Thank you:-)
But how you do it?please please explain it to me.
To find the domain of these functions, we need to consider the values of x for which the functions are defined.
1)
a) For the sum of two functions (f + g), we need both f(x) and g(x) to be defined. In this case, f(x) = 9x - 2 and g(x) = √(3x + 7). Since square roots are only defined for non-negative values, we need to ensure that 3x + 7 ≥ 0, which means x ≥ -7/3. Thus, the domain of (f + g) is all real numbers greater than or equal to -7/3.
b) For the product of two functions (fg), again, we need both f(x) and g(x) to be defined. In this case, the functions are defined for all real numbers, so the domain of fg is also all real numbers.
c) Finally, for the division of two functions (f/g), we need g(x) to be defined and not equal to zero. Since g(x) = √(3x + 7), we need 3x + 7 > 0 to avoid taking the square root of a negative number. This means x > -7/3. Additionally, we need g(x) to be nonzero, which means 3x + 7 ≠ 0. Solving this inequality gives us x ≠ -7/3. Therefore, the domain of f/g is all real numbers except -7/3.
2) To compute the value of (f o g o f)(2), we need to follow the composition of functions.
First, substitute x = 2 into the function g(x):
g(2) = √(3(2) + 7) = √(6 + 7) = √13.
Next, substitute this value into the function f(x):
f(g(2)) = f(√13) = 3(√13) - 2 = 3√13 - 2.
So, the value of (f o g o f)(2) is 3√13 - 2.