Advertisements
Advertisements
Question
Let f and g be real functions defined by f(x) = 2x + 1 and g(x) = 4x – 7. For what real numbers x, f(x) = g(x)?
Solution
f and g be real functions defined by f(x) = 2x + 1 and g(x) = 4x – 7
To satisfy the condition f(x) = g(x)
Should also satisfy
2x + 1 = 4x – 7
⇒ 7 + 1 = 4x – 2x
⇒ 8 = 2x
Or, 2x = 8
⇒ x = 4
Hence, we get
For x = 4, f(x) = g(x)
APPEARS IN
RELATED QUESTIONS
Let f, g: R → R be defined, respectively by f(x) = x + 1, g(x) = 2x – 3. Find f + g, f – g and `f/g`
Let f = {(1, 1), (2, 3), (0, –1), (–1, –3)} be a function from Z to Z defined by f(x) = ax + b, for some integers a, b. Determine a, b.
Let R be a relation from N to N defined by R = {(a, b): a, b ∈ N and a = b2}. Is the following true?
(a, a) ∈ R, for all a ∈ N
Justify your answer in case.
Find x and y if: (4x + 3, y) = (3x + 5, – 2)
If f and g are real functions defined by f(x) = x2 + 7 and g(x) = 3x + 5, find the following:
`f(1/2) xx g(14)`
If f and g are real functions defined by f(x) = x2 + 7 and g(x) = 3x + 5, find the following:
f(– 2) + g(– 1)
If f and g are real functions defined by f(x) = x2 + 7 and g(x) = 3x + 5, find the following:
f(t) – f(– 2)
If f and g are real functions defined by f(x) = x2 + 7 and g(x) = 3x + 5, find the following:
`(f(t) - f(5))/(t - 5)`, if t ≠ 5
Let f and g be real functions defined by f(x) = 2x + 1 and g(x) = 4x – 7. For what real numbers x, f(x) < g(x)?
If f and g are two real valued functions defined as f(x) = 2x + 1, g(x) = x2 + 1, then find `f/g`
Find the values of x for which the functions f(x) = 3x2 – 1 and g(x) = 3 + x are equal.
Is g = {(1, 1), (2, 3), (3, 5), (4, 7)} a function? Justify. If this is described by the relation, g(x) = αx + β, then what values should be assigned to α and β?
Let f and g be two real functions given by
f = {(0, 1), (2, 0), (3, – 4), (4, 2), (5, 1)}
g = {(1, 0), (2, 2), (3, – 1), (4, 4), (5, 3)}
then the domain of f . g is given by ______.
Let f = {(2, 4), (5, 6), (8, – 1), (10, – 3)}
g = {(2, 5), (7, 1), (8, 4), (10, 13), (11, 5)}
be two real functions. Then Match the following :
| Column A | Column B |
| f – g | `{(2, 4/5), (8, (-1)/4), (10, (-3)/13)}` |
| f + g | {(2, 20), (8, −4), (10, −39)} |
| f . g | {(2, −1), (8, −5), (10, −16)} |
| `f/g` | {(2, 9), (8, 3), (10, 10)} |
Let a real valued function f(x) satisfying f(x + y) + f(x – y) = f(x)f(y) {f(0) ≠ 0} ∀ x, y ∈ R, then f(–2) – f(–1) + f(0) + f(1) – f(2) is equal to ______.
Let f: `R - {1/2}→R - {1/2}, f(x) = (x - 2)/(2x - 1)` be a function such that x = m is the solution of f(x) + 2f–1(x) + 2 = f(f(x)), then m is equal to ______.
Let f(x) be a function which satisfies f(x3)f’(x) = f’(x)f’(x3) + f”(x2). Given that f(1) = 1 and f”’(1) = `1/4`, then value of 4(f’(1) + f'”(1)) is ______.
