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${:[f(x)=3x^(2)+4x-2],[g(x)=7x^(2)-bx+3]:} If f(x)-g(x)=-4x^(2)+6x-5 for all values of x where b is a constant, then what is the value of b ? Choose 1 answer: (A) -10 (B) -2 (c) 2 (D) 10$

$\begin{array}{l} f(x)=3 x^{2}+4 x-2 \\ g(x)=7 x^{2}-b x+3 \end{array}$ $\newline$ If $\newline$ $f(x)-g(x)=-4 x^{2}+6 x-5$ $\newline$ for all values of $x$ where $b$ is a constant, then what is the value of $b$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $-10$ $\newline$ (B) $-2$ $\newline$ (C) $2$ $\newline$ (D) $10$

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Compare linear and exponential growth

Full solution

Q.

\begin{array}{l} f(x)=3 x^{2}+4 x-2 \\ g(x)=7 x^{2}-b x+3 \end{array}

\newline

If

\newline

f(x)-g(x)=-4 x^{2}+6 x-5

\newline

for all values of

x

where

b

is a constant, then what is the value of

b

?

\newline

Choose

1

answer:

\newline

(A)

-10

\newline

(B)

-2

\newline

(C)

2

\newline

(D)

10

Given Functions: We are given two functions: $\newline$ $f(x) = 3x^2 + 4x - 2$ $\newline$ $g(x) = 7x^2 - bx + 3$ $\newline$ And we know that: $\newline$ $f(x) - g(x) = -4x^2 + 6x - 5$ $\newline$ To find the value of $b$ , we need to subtract $g(x)$ from $f(x)$ and compare the result to the given expression for $f(x) - g(x)$ .
Subtracting $f(x)$ and $g(x)$ : Let's perform the subtraction: $\newline$ $f(x) - g(x) = (3x^2 + 4x - 2) - (7x^2 - bx + 3)$ $\newline$ Simplify the expression by distributing the negative sign and combining like terms: $\newline$ $f(x) - g(x) = 3x^2 + 4x - 2 - 7x^2 + bx - 3$ $\newline$ $f(x) - g(x) = -4x^2 + (4 + b)x - 5$
Comparing Coefficients: Now we compare the coefficients of the resulting expression with the given expression for $f(x) - g(x)$ : $-4x^2 + (4 + b)x - 5 = -4x^2 + 6x - 5$ The coefficients of $x^2$ and the constant terms are already equal on both sides, so we only need to compare the coefficients of $x$ : $4 + b = 6$
Solving for b: To find the value of b, we solve the equation: $\newline$ $4 + b = 6$ $\newline$ Subtract $4$ from both sides: $\newline$ $b = 6 - 4$ $\newline$ $b = 2$

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\newline

\newline

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f(x)

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\newline

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\newline

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h'(8)

\newline

Simplify any fractions.

\newline

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p(x)

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are differentiable.

\newline

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\newline

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\newline

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a(x)

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\newline

c(x)

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\newline

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c'(2)

\newline

Simplify any fractions.

\newline

c'(2)=

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\newline

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\newline

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\newline

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\newline

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