If \( f(x+5)=x^{2}-5 x+7 \) find \( f(x) \) A. \( f(x)=x^{2}-15 x+37

1.	If \( f(x+5)=x^{2}-5 x+7 \) find \( f(x) \) A. \( f(x)=x^{2}-15 x+37 \)B. \( f(x)=x^{2}+15 x+57 \) C. \( f(x)=x^{2}-15 x+37 \)D. \( f(x)=x^{2}-15 x+57 \)
Answer» Correct answer is:- (D) f(x) = x² - 15x + 57 Explanation:- Let, f(x) = ax² + bx + c... (1) Now, f(x + 5) = a(x + 5)² + b(x + 5) + c x² - 5x + 7 = ax² +10ax + 25a + bx + 5b + c. Comparing the coefficient of x², we get a = 1, x² - 5x + 7 = x² + 10x + 25 + bx + 5b + c -15x - 18 = bx + 5b + c, Comparing the coefficient of x, we get b = -15, -15x - 18 = -15x - 75 + c c = 57. Putting the values of a, b and c in (1) we get, f(x) = x² - 15x + 57. Therefore, the required polynomial is x² - 15x + 57 (D) x² - 15x + 57 f(x + 5) = x² - 5x + 7 \(\therefore\) f(x) = (x - 5)² - 5(x - 5) + 7 (By taking x -5 as x) = x² - 10x + 25 - 5x + 25 + 7 = x² - 15x + 57

If \( f(x+5)=x^{2}-5 x+7 \) find \( f(x) \) A. \( f(x)=x^{2}-15 x+37 \)B. \( f(x)=x^{2}+15 x+57 \) C. \( f(x)=x^{2}-15 x+37 \)D. \( f(x)=x^{2}-15 x+57 \)

Answer»

Correct answer is:- (D) f(x) = x² - 15x + 57

Explanation:- Let,

f(x) = ax² + bx + c... (1)

Now, f(x + 5) = a(x + 5)² + b(x + 5) + c

x² - 5x + 7 = ax² +10ax + 25a + bx + 5b + c.

Comparing the coefficient of x², we get a = 1,

x² - 5x + 7 = x² + 10x + 25 + bx + 5b + c

-15x - 18 = bx + 5b + c,

Comparing the coefficient of x, we get b = -15,

-15x - 18 = -15x - 75 + c

c = 57.

Putting the values of a, b and c in (1) we get,

f(x) = x² - 15x + 57.

Therefore, the required polynomial is x² - 15x + 57

(D) x² - 15x + 57

f(x + 5) = x² - 5x + 7

\(\therefore\) f(x) = (x - 5)² - 5(x - 5) + 7 (By taking x -5 as x)

= x² - 10x + 25 - 5x + 25 + 7

= x² - 15x + 57

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