If f(x) = x² – 3 and g (x) = -x + 3, determine where g(x) > f(x). %3D %3D

Q: Find the domain of the function.

A: Given:            fx=1-2x The function is defined for 1-2x≥0

Q: For the functions f(x) = - 4x+1 and g(x) = 2x-x+5, find g(f(- 2)). %3D %3D (f(-2)) = %3D

A: A composite function is created when one function is substituted into another function.  f∘gx =fgx

Q: the functionf and g are given by f(x)= x – 1 and g(x) = x², then D, =

A: Answer and explanation is given below....

Q: Let f(x) = V2 - x+ 8. Determine f-(x) and the the domain of f(z). f(x) = %3D Domain of f-(æ) =

A:

Q: Let f(x) = - 4x- 1, h(x) = -x- 4. = -x-4. %3D Find (f o h)(- 5). (f o h)( – 5) = | 19 o

A: Here given as fx=-4x-1, hx=-x-4 Now  fohx=fhx=f-x-4=-4-x-4-1=4x+16-1=4x+15

Q: Let f(x) = - 9x + 12 and g(x) = x2 + 6. %3D Find f(5) + g(5).

A: Given that f(x)=-9x+12.       and g(x)=x2 + 6 find f(5)+g(5)

Q: Let f(x) = 8 – 5x + 11x. Calculate the following values: %3D f(a) = f(a + h) = f(a + h) – f(a) for h…

A:

Q: a. Find ux b. Find uy C. Show that u satisfies the partial differential equation xux + yuy = 3u. %3D

A: In this question we have to find differentiation for the for the following question.

Q: X If f(x) = /x, g(x) = 3 and h(x) = 3x + 9, find f(g(h(x))). |

A: Given the functionsf(x)=x,g(x)=x3 and h(x)=3x+9

Q: Consider the function f(x) = Ax³ + Bx² + 5x. Find the values of A and B if f'(-2) = -3 and f" (-2) =…

A: f(x)=Ax3+Bx2+5x

Q: 4. Graph the functions f (x) = 2(x + 6)² + 2 and its inverse.

A: The given function is f(x) = 2(x+6)2 + 2  When we put x = 0, the value of f(x) comes out to be…

Q: Vx² + 1 +x lim X ∞ 4xr -1 II

A:

Q: Use the functions, f (x) = 2x + 3 and g(x) = –x² + 5x and h(x) = x + 4 to find f (g(h(x))). %3D %3D

A: Given : f(x) = 2x + 3g(x) = -x2 + 5xh(x) = x + 4

Q: Find the domains and ranges F(X)= %3D -X-4X-3

A: Given,  FX = -X2-4X-3  We have to find the domain and range of function.

Q: If f(x) = x - 3 and g(x) = x² + 4, simplify (f g)(x).

A: We know, (f∘g)(x)=f{g(x)} Gvbhj

Q: Let f(x) = - 9x + 20 and g(x) = x² + 8. Find f(- 5) • g(- 5). f(- 5) • g(- 5) =

A:

Q: Let f = {(5,3),(8,9),(3,8)} and g = 5x +4. Find f(3) + g(3). %3D

A: Given that f = { (5, 3), (8, 9), (3, 8) } Clearly we can say that f(3) = 8 as (3,8) belongs to f

Q: Let f(x) = -3x² and g(x) = 2x – 6. Find and simplify_the following. | g(f(x)) = b. f(g(x)) =

A: f(x)=-3x2, g(x)=2x-6a) g(f(x))=g(-3x2)=2(-3x2)-6=-6x2-6g(f(x))=-6x2-6