Chapter 5: Q. 62 (page 257)

If $f (x) = 3 x^{2} - 7$ and $g (x) = 2 x + a$ , find $a$ so that the graph of $f \circ g$ crosses the y-axis at 68.

Short Answer

Expert verified

The value of $a$ is $\pm 5 .$

Step by step solution

Step 1. Given Information

Given that $f (x) = 3 x^{2} - 7$ and $g (x) = 2 x + a,$ value of $f \circ g (x)$ at $x = 0$ is 68.

Step 2. Solution

We know that $f \circ g (x) = f (g (x)) .$

Here, $f (x) = 3 x^{2} - 7, g (x) = 2 x + a$

$f \circ g (x) = f (g (x)) f \circ g (x) = 3 (g {(x))}^{2} - 7 f \circ g (x) = 3 {2 x + a}^{2} - 7 f \circ g (x) = 3 {4 x^{2} + 4 x a + a^{2}} - 7 f \circ g (x) = 12 x^{2} + 12 x a + 3 a^{2} - 7$

So, at $x = 0$ , $f \circ g (0) = 68 .$

Now,

$f \circ g (x) = 12 x^{2} + 12 x a + 3 a^{2} - 7, a t x = 0 f \circ g (0) = 12 {(0)}^{2} + 12 (0) (a) + 3 a^{2} - 7 68 = 0 + 0 + 3 a^{2} - 7 3 a^{2} = 68 + 7 3 a^{2} = 75 a^{2} = 25 a = \pm 5 .$

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If $f (x) = 3 x^{2} - 7$ and $g (x) = 2 x + a$ , find $a$ so that the graph of $f \circ g$ crosses the y-axis at 68.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Solution

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If f(x)=3x2-7and g(x)=2x+a, find aso that the graph off∘g crosses the y-axis at 68.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Solution

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Most popular questions from this chapter

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If $f (x) = 3 x^{2} - 7$ and $g (x) = 2 x + a$ , find $a$ so that the graph of $f \circ g$ crosses the y-axis at 68.