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2 years ago

For f(x)=4x+1 and g(x)=x^2-5 find (fog)(x)

Mathematics

2 answers:

d1i1m1o1n [39]2 years ago

5 0

Answer:

(fog)(x) = $4x^{2}-19$

Step-by-step explanation:

The given functions are f(x) = 4x + 1 and g(x) = $x^{2}-5$

We have to find the value of (fog)(x).

Since (fog)(x) = f[g(x)]

It means we have to find the value of f(x) for the value of x = g(x)

Now f[g(x)] = $4[x^{2}-5]+1$

= $4x^{2}-20+1$

= $4x^{2}-19$

Therefore, f[g(x)] = $4x^{2}-19$ will be the answer.

lara [203]2 years ago

3 0

(fog)(x)= f(g(x))= 4(x^2-5)+1= (4•x^2)-20+1=

(4•x^2)-19

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A school bus has 25 seats, with 5 rows of 5 seats. 15 students from the first grade and 5 students from the second grade travel

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2 years ago

Vertex A in quadrilateral ABCD lies at (-3, 2). If you rotate ABCD 180° clockwise about the origin, what will be the coordinates

Marysya12 [62]

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A company makes a product and has no way to determine which ones are faulty until an unhappy customer returns it. Three percent

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Sum of positive roots of the equation (x2 - 12x + 35) (x2 + 10x + 24) = 504 is

Digiron [165]

Answer:

(3)11

Step-by-step explanation:

We are given that

$(x^2-12x+35)(x^2+10x+24)=504$

We have to find the sum of positive roots of the equation.

$x^2(x^2+10x+24)-12x(x^2+10x+24)+35(x^2+10x+24)=504$

$x^4+10x^3+24x^2-12x^3-120x^2-288x+35x^2+350x+840=504$

$x^4-2x^3-61x^2+62x+840-504=0$

$x^4-2x^3-61x^2+62x+336=0$

Factor of 336

2,3,4,6,8,7,

Let x=2

$2^4-2^4-61(2^2)+62(2)+336\neq0$

x=2 is not the root of equation

x=-2

$(-2)^4-2(-2)^3-61(-2)^2+62(-2)+336=0$

Hence x=-2 is the root of equation.

x+2 is a factor of equation.

x=3

$3^4-2(3^3)-61(3^2)+62(3)+336=0$

Therefore, x=3 is the root of equation.

$(x+2)(x-3)(x^2-x-56)=0$

$(x+2)(x-3)(x^2-8x+7x-56)=0$

$(x+2)(x-3)(x(x-8)+7(x-8))=0$

$(x+2)(x-3)(x-8)(x+7)=0$

$x-8=0\implies x=8$

$x+7=0\implies x=-7$

Positive roots are 3 and 8

Sum of positive roots=3+8=11

Option (3) is true.

4 0

2 years ago