4. If f(x) and g(x) are continuous on [a, b], which one of the following statements is true? [f{x)– g(x)]dx = ] f(x)dx -fg(x)dx %3D f(x)dx =2[f(x)dx Sf(x)dx O j3+f(x)dx =3+ƒf(x)dx

Q: Find the domain of the following function 1 f (x) = 2 + f (x) Vx

A: Given function,                            f(x)=12+x

Q: 8. Find f-1 (x) for f (x) = 2-4

A:

Q: Show that f[x0, x1, x2] = f[x2, x1, xo].

A:

Q: snip

A: If f(x)=ax, Then to show that, f(αx)=f(x)α

Q: 2.if f (x) = x2 + 3, with domain R then f(x) has f(x) %3D O T F

A: Here the given function is f(x)= x2+3 with domain R We need to find it has inverse or not.

Q: 1. How to define the function, f(x, y) = 15x+4x*y+15y 3x+3y to make it a continues function?

A: We have to find the given function is continuous.

Q: If f is a continuous function, then 02/1² f(x) dx °S ² ƒ(² f(x) dx : [*²* xf(x) dx √2 [²³² f(x) dx 2…

A:

Q: IfY C X, show that inf (X) < inf (Y)

A:

Q: 3. Find f(x) and f (x) if f(x) = lnx + 2cos³ x. %3D

A: First use sum/difference rule of differentiation f±g=f'±g' then use the following formulae: dln…

Q: For what values of x is Ax) concave down if f "(x) = 3x' – 14x² + &r?

A: Given that, f''x=3x3-14x2+8x For what value of x is fx concave down.

Q: The function f(x)=(2-x)/(3) is continuous at

A:

Q: Let f(x) = 8 - x f-¹(x)

A:

Q: The function x2 f(x) = 1 - x is decreasing on (0, 1). Select one: O True O False

A:

Q: Let f(x) f-¹(-2) = x + 3 x + 6

A:

Q: Suppose f is a real function satisfying f(x + f(x)) = 4ƒ(x) and ƒ(1) = 4. What is ƒ(21)? f(21)=

A: Suppose f is a real function satisfying f(x+ f(x))= 4f(x) and f(1) = 4, what is f(21)?

Q: Let f(x) ƒ-¹(x) = = 1 x + 13

A:

Q: 58. Show that if f is a function and z = x+h, then f(2) – f(x) _ f(x+ h) – f(x) Z - x h

A: This question is taken from the function in which we have to prove the given equation. We can write…

Q: Show that the function f(x)=√x+1 is differentiable in 2 = 2 but not differentiable in x = −1.

A: Given data:- The given function is, fx=x+1

Q: Two functions f, g are defined as follows: Find a) ƒ-¹(2) b) (gof)(-4) f(x) = 3x + 5 g(x) = 2(1-x)

A: