Their debut studio album, Pinocchio (2011), and their two extended plays Nu Abo and Electric Shock produced three number-one singles on South Korea's Gaon Digital Chart.

In August 2019, f(x) officially reunited as a three-piece (without Victoria) and performed at the three-night SM Town Live 2019 in Tokyo concert.

It is used to symbolize their various activities, based on the various talents and attractiveness of the members, like a function in which the output or results change depending on the input value of x.

[5] Krystal was scouted by SM Entertainment in 2000 while on a family visit to Korea, along with her sister Jessica (who would go on to be a member of Girls' Generation).

She subsequently appeared in a small role in Shinhwa's music video for the song "Wedding March" ("너의 곁에서 2").

[6][7] Sulli was a child actress, making her first television appearance in 2005 as the young Princess Seonhwa of Silla in SBS's Ballad of Seodong.

[11][12][13] Their debut single "La Cha Ta" was released on September 1, with a showcase held the following day at Samseong Fashion Center in Gangnam.

[16][17] A month later, the group appeared as special guests at Girls' Generation's Into The New World concert at the Olympic Fencing Gymnasium, Seoul.

In June, Amber went on hiatus due to an ankle injury, while the remaining members continued group activities without her for the remainder of the year.

Towards the end of 2010 it was announced that f(x)'s albums would be distributed under Japanese label Avex Entertainment in Japan, Taiwan, China, and Hong Kong.

The repackaged album contained the title track "Hot Summer" (a remake of a Monrose song produced by Thomas Troelsen and Remee), as well as three previously released digital singles: "LA chA TA", "Chu~♡", and "Is It Ok?".

[31][32] Shortly after the album was released, it was announced that Sulli was unable to perform with the group for health reasons, and that she would be taking a temporary hiatus.

[44][unreliable source] In an interview with Krystal on January 19, 2018, she stated that the members frequently discussed making a comeback but timing never worked out.

[53] On April 23, during a review video of her activities from debut to present, Luna expressed confusion over f(x) being referred to in the past tense, stating that the group had not yet disbanded.

In 2015, while reviewing 4 Walls, American music magazine Spin called f(x) the "world's greatest living pop group" at the time.

Billboard also noted that "Ice Cream Cake" represents a baton pass from f(x) to Red Velvet as the best idol group alive, meaning that f(x) was the former holder of the title.