Answer:
Domain and Range of g(f(x)) are 'All real numbers' and {y | y>6 } respectively
Step-by-step explanation:
We have the functions, f(x) = eˣ and g(x) = x+6
So, their composition will be g(f(x)).
Then, g(f(x)) = g(eˣ) = eˣ+6
Thus, g(f(x)) = eˣ+6.
Since the domain and range of f(x) = eˣ are all real numbers and positive real numbers respectively.
Moreover, the function g(f(x)) = eˣ+6 is the function f(x) translated up by 6 units.
Hence, the domain and range of g(f(x)) are 'All real numbers' and {y | y>6 } respectively.
Answer:
Please check the explanation.
Step-by-step explanation:
Given
a)
f(x) + g(x) = (2x - 1) + (2 - x)
= 2x -1 + 2 - x
= x + 1
b)
f(x) - g(x) = (2x - 1) - (2 - x)
= 2x - 1 - 2 + x
= 3x - 3
c)
g(-5) - f(-5)
Putting x = -5 in g(x) = 2 - x
g(x) = 2 - x
g(-5) = 2 - (-5) = 2+5 = 7
Putting x = -5 in f(x) = 2x - 1
f(x) = 2x - 1
f(-5) = 2(-5) - 1
= -10 - 1
= -11
Thus,
g(-5) - f(-5) = 7 - (-11) = 7+11 = 18
d)
f(x).g(x) = (2x - 1) (2 - x) = -2x² + 5x - 2
e)
f(g(x)) = f(2-x)
= 2(2-x)-1
= 4-2x-1
= 3-2x
According to the given information, the equation represents a line that is tangent to the circle and goes through the point W is given by:
y = -x + 6.
<h3>What is the equation of the circle?</h3>
The equation of a circle of center 
and radius r is given by:
In this problem, we have that the center is at point (0,2), hence:
It goes through point (3,3), hence:
Hence, the equation is:
<h3>What is the equation of the tangent line at point W?</h3>
It is given by:
Applying implicit differentiation, we have that:
Point W(3,3), hence:
Hence the equation is:
y - 3 = -(x - 3).
y = -x + 6.
More can be learned about the equation of a tangent line at brainly.com/question/8174665
Answer:
answer given in step by step...
Step-by-step explanation:
13x+13(x+1)+13(x+2)=312
13x+13x+13+13x+26=312
39x+39=312
39x=312-39
39x=273
x=7
first number=13x=13*7=91
second number=13(8)=104
third number=13(9)=117
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